Mathematics Books
Springer New York Modern Geometry Methods and Applications
Book SynopsisThis is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory.Table of Contents1 Geometry in Regions of a Space. Basic Concepts.- §1. Co-ordinate systems.- 1.1. Cartesian co-ordinates in a space.- 1.2. Co-ordinate changes.- §2. Euclidean space.- 2.1. Curves in Euclidean space.- 2.2. Quadratic forms and vectors.- §3. Riemannian and pseudo-Riemannian spaces.- 3.1. Riemannian metrics.- 3.2. The Minkowski metric.- §4. The simplest groups of transformations of Euclidean space.- 4.1. Groups of transformations of a region.- 4.2. Transformations of the plane.- 4.3. The isometries of 3-dimensional Euclidean space.- 4.4. Further examples of transformation groups.- 4.5. Exercises.- §5. The Serret—Frenet formulae.- 5.1. Curvature of curves in the Euclidean plane.- 5.2. Curves in Euclidean 3-space. Curvature and torsion.- 5.3. Orthogonal transformations depending on a parameter.- 5.4. Exercises.- §6. Pseudo-Euclidean spaces.- 6.1. The simplest concepts of the special theory of relativity.- 6.2. Lorentz transformations.- 6.3. Exercises.- 2 The Theory of Surfaces.- §7. Geometry on a surface in space.- 7.1. Co-ordinates on a surface.- 7.2. Tangent planes.- 7.3. The metric on a surface in Euclidean space.- 7.4. Surface area.- 7.5. Exercises.- §8. The second fundamental form.- 8.1. Curvature of curves on a surface in Euclidean space.- 8.2. Invariants of a pair of quadratic forms.- 8.3. Properties of the second fundamental form.- 8.4. Exercises.- §9. The metric on the sphere.- §10. Space-like surfaces in pseudo-Euclidean space.- 10.1. The pseudo-sphere.- 10.2. Curvature of space-like curves in $$ \mathbb{R}_1^3 $$.- §11. The language of complex numbers in geometry.- 11.1. Complex and real co-ordinates.- 11.2. The Hermitian scalar product.- 11.3. Examples of complex transformation groups.- §12. Analytic functions.- 12.1. Complex notation for the element of length, and for the differential of a function.- 12.2. Complex co-ordinate changes.- 12.3. Surfaces in complex space.- §13. The conformal form of the metric on a surface.- 13.1. Isothermal co-ordinates. Gaussian curvature in terms of conformal co-ordinates.- 13.2. Conformal form of the metrics on the sphere and the Lobachevskian plane.- 13.3. Surfaces of constant curvature.- 13.4. Exercises.- §14. Transformation groups as surfaces in N-dimensional space.- 14.1. Co-ordinates in a neighbourhood of the identity.- 14.2. The exponential function with matrix argument.- 14.3. The quaternions.- 14.4. Exercises.- §15. Conformal transformations of Euclidean and pseudo-Euclidean spaces of several dimensions.- 3 Tensors: The Algebraic Theory.- §16. Examples of tensors.- §17. The general definition of a tensor.- 17.1. The transformation rule for the components of a tensor of arbitrary rank.- 17.2. Algebraic operations on tensors.- 17.3. Exercises.- §18. Tensors of type (0, k).- 18.1. Differential notation for tensors with lower indices only.- 18.2. Skew-symmetric tensors of type (0, k).- 18.3. The exterior product of differential forms. The exterior algebra.- 18.4. Skew-symmetric tensors of type (k, 0) (polyvectors). Integrals with respect to anti-commuting variables.- 18.5. Exercises.- §19. Tensors in Riemannian and pseudo-Riemannian spaces.- 19.1. Raising and lowering indices.- 19.2. The eigenvalues of a quadratic form.- 19.3. The operator ?.- 19.4. Tensors in Euclidean space.- 19.5. Exercises.- §20. The crystallographic groups and the finite subgroups of the rotation group of Euclidean 3-space. Examples of invariant tensors.- §21. Rank 2 tensors in pseudo-Euclidean space, and their eigenvalues.- 21.1. Skew-symmetric tensors. The invariants of an electromagnetic field.- 21.2. Symmetric tensors and their eigenvalues. The energy-momentum tensor of an electromagnetic field.- §22. The behaviour of tensors under mappings.- 22.1. The general operation of restriction of tensors with lower indices.- 22.2. Mappings of tangent spaces.- §23. Vector fields.- 23.1. One-parameter groups of diffeomorphisms.- 23.2. The exponential function of a vector field.- 23.3. The Lie derivative.- 23.4. Exercises.- §24. Lie algebras.- 24.1. Lie algebras and vector fields.- 24.2. The fundamental matrix Lie algebras.- 24.3. Linear vector fields.- 24.4. Left-invariant fields defined on transformation groups.- 24.5. Invariant metrics on a transformation group.- 24.6. The classification of the 3-dimensional Lie algebras.- 24.7. The Lie algebras of the conformal groups.- 24.8. Exercises.- 4 The Differential Calculus of Tensors.- §25. The differential calculus of skew-symmetric tensors.- 25.1. The gradient of a skew-symmetric tensor.- 25.2. The exterior derivative of a form.- 25.3. Exercises.- §26. Skew-symmetric tensors and the theory of integration.- 26.1. Integration of differential forms.- 26.2. Examples of integrals of differential forms.- 26.3. The general Stokes formula. Examples.- 26.4. Proof of the general Stokes formula for the cube.- 26.5. Exercises.- §27. Differential forms on complex spaces.- 27.1. The operators d? and d?.- 27.2. Kählerian metrics. The curvature form.- §28. Covariant differentiation.- 28.1. Euclidean connexions.- 28.2. Covariant differentiation of tensors of arbitrary rank.- §29. Covariant differentiation and the metric.- 29.1. Parallel transport of vector fields.- 29.2. Geodesics.- 29.3. Connexions compatible with the metric.- 29.4. Connexions compatible with a complex structure (Hermitian metric).- 29.5. Exercises.- §30. The curvature tensor.- 30.1. The general curvature tensor.- 30.2. The symmetries of the curvature tensor. The curvature tensor defined by the metric.- 30.3. Examples: The curvature tensor in spaces of dimensions 2 and 3; the curvature tensor of transformation groups.- 30.4. The Peterson—Codazzi equations. Surfaces of constant negative curvature, and the “sine—Gordon” equation.- 30.5. Exercises.- 5 The Elements of the Calculus of Variations.- §31. One-dimensional variational problems.- 31.1. The Euler—Lagrange equations.- 31.2. Basic examples of functional.- §32. Conservation laws.- 32.1. Groups of transformations preserving a given variational problem.- 32.2. Examples. Applications of the conservation laws.- §33. Hamiltonian formalism.- 33.1. Legendre’s transformation.- 33.2. Moving co-ordinate frames.- 33.3. The principles of Maupertuis and Fermat.- 33.4. Exercises.- §34. The geometrical theory of phase space.- 34.1. Gradient systems.- 34.2. The Poisson bracket.- 34.3. Canonical transformations.- 34.4. Exercises.- §35. Lagrange surfaces.- 35.1. Bundles of trajectories and the Hamilton—Jacobi equation.- 35.2. Hamiltonians which are first-order homogeneous with respect to the momentum.- §36. The second variation for the equation of the geodesics.- 36.1. The formula for the second variation.- 36.2. Conjugate points and the minimality condition.- 6 The Calculus of Variations in Several Dimensions. Fields and Their Geometric Invariants.- §37. The simplest higher-dimensional variational problems.- 37.1. The Euler—Lagrange equations.- 37.2. The energy-momentum tensor.- 37.3. The equations of an electromagnetic field.- 37.4. The equations of a gravitational field.- 37.5. Soap films.- 37.6. Equilibrium equation for a thin plate.- 37.7. Exercises.- §38. Examples of Lagrangians.- §39. The simplest concepts of the general theory of relativity.- §40. The spinor representations of the groups SO(3) and O(3, 1). Dirac’s equation and its properties.- 40.1. Automorphisms of matrix algebras.- 40.2. The spinor representation of the group SO(3).- 40.3. The spinor representation of the Lorentz group.- 40.4. Dirac’s equation.- 40.5. Dirac’s equation in an electromagnetic field. The operation of charge conjugation.- §41. Covariant differentiation of fields with arbitrary symmetry.- 41.1. Gauge transformations. Gauge-invariant Lagrangians.- 41.2. The curvature form.- 41.3. Basic examples.- §42. Examples of gauge-invariant functionals. Maxwell’s equations and the Yang—Mills equation. Functionals with identically zero variational derivative (characteristic classes).
£40.79
Springer-Verlag New York Inc. Differential Equations and Their Applications
Book SynopsisChapter 1 First-order differential equations * Chapter 2 Second-order linear differential equations * Chapter 3 Systems of differential equations * Chapter 4 Qualitative theory of differential equations * Chapter 5 Separation of variables and Fourier series * Chapter 6 Sturm -Liouville boundary value problems * Appendix A Some simple facts concerning functions of several variables * Appendix B Sequences and series * Appendix C C Programs * Answers to odd-numbered exercises * IndexTable of ContentsChapter 1 First-order differential equations * Chapter 2 Second-order linear differential equations * Chapter 3 Systems of differential equations * Chapter 4 Qualitative theory of differential equations * Chapter 5 Separation of variables and Fourier series * Chapter 6 Sturm -Liouville boundary value problems * Appendix A Some simple facts concerning functions of several variables * Appendix B Sequences and series * Appendix C C Programs * Answers to odd-numbered exercises * Index
£46.74
Springer Riemannian Manifolds
Book SynopsisWhat Is Curvature?.- Review of Tensors, Manifolds, and Vector Bundles.- Definitions and Examples of Riemannian Metrics.- Connections.- Riemannian Geodesics.- Geodesics and Distance.- Curvature.- Riemannian Submanifolds.- The Gauss-Bonnet Theorem.- Jacobi Fields.- Curvature and Topology.Trade Review"This book is very well writen, pleasant to read, with many good illustrations. It deals with the core of the subject, nothing more and nothing less. Simply a recommendation for anyone who wants to teach or learn about the Riemannian geometry."Nieuw Archief voor Wiskunde, September 2000Table of ContentsWhat Is Curvature?.- Review of Tensors, Manifolds, and Vector Bundles.- Definitions and Examples of Riemannian Metrics.- Connections.- Riemannian Geodesics.- Geodesics and Distance.- Curvature.- Riemannian Submanifolds.- The Gauss-Bonnet Theorem.- Jacobi Fields.- Curvature and Topology.
£51.29
Springer New York Lectures on Modules and Rings
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Springer-Verlag New York Inc. Introduction to Mechanics and Symmetry
Book SynopsisSpecific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering.Trade Review"The book is self-contained.It remains a good and solid introduction to this subject."Nieuw Archief voor Wiskunde, March 2001 "... This book takes the reader on one of the greatest journeys in modern mathematics that has as its roots a subject that is more than 300 years old. Armed with this knowledge a reader is ready to pursue numerous topics of active mathematical research, from the more pure domains of symplectic geometry and topology to the geometric analysis of the limitless supply of examples from mechanics."Newsletter of the Newzealand Mathematical Society, No. 81, April 2001 Second Edition J.E. Marsden and T.S. Ratiu Introduction to Mechanics and Symmetry A Basic Exposition of Classical Mechanical Systems "As the name of the book implies, a consistent theme running through the book is that of symmetry. Indeed the latter half of the book focuses on Poisson manifolds, momentum maps, Lie-Poisson reduction, co-adjoint orbits and the integrability of the rigid body. The discussion of reduction must be the most comprehensive yet given. A pleasant feature of the book is that most of the theory that relates to finite-dimensional mechanical systems is illustrated concretely in terms of local coordinates, thereby making the book accessible even to beginners in the field."—MATHEMATICAL REVIEWSTable of ContentsPreface * About the Authors * 1 Introduction and Overview * 2 Hamiltonian Systems on Linear Symplectic Spaces * 3 An Introduction to Infinite-Dimensional Systems * 4 Manifolds, Vector Fields, and Differential Forms * 5 Hamiltonian Systems on Symplectic Manifolds * 6 Cotangent Bundles * 7 Lagrangian Mechanics * 8 Variational Principles, Constraints, and Rotating Systems * 9 An Introduction to Lie Groups * 10 Poisson Manifolds * 11 Momentum Maps *12 Computation and Properties of Momentum Maps * 13 Lie-Poisson and Euler-Poincare Reduction * 14 Coadjoint Orbits * 15 The Free Rigid Body * References
£67.49
Springer New York Modeling Survival Data Extending the Cox Model Statistics for Biology and Health
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W. W. Norton & Company 21st Century Astronomy The Solar System
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W. W. Norton & Company 21st Century Astronomy Stars and Galaxies 5e
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WW Norton & Co GameChanger
Book SynopsisEmpowers readers with the wisdom to win in every strategic situation.Trade Review"...a well-written account of wide-ranging real-world situations that show the nuts and bolts of game theory..." -- Engineering & Technology
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W. W. Norton & Company Learning Astronomy by Doing Astronomy
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W. W. Norton & Company 21st Century Astronomy
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W. W. Norton & Company 21st Century Astronomy
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W. W. Norton & Company 21st Century Astronomy Stars Galaxies with
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W. W. Norton & Company Physics for Engineers and Scientists
Book SynopsisDesigned for the introductory calculus-based physics course, Physics for Engineers and Scientists is distinguished by its lucid exposition and accessible coverage of fundamental physical concepts.
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W. W. Norton & Company Physics for Engineers V 3 Chapters 3641
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WW Norton & Co Principles of Physics
Book SynopsisPrinciples of Physics is a textbook for a one year algebra-based introduction physics course. The book is intended for students in the life sciences, the premedical curriculum, the earth and environmental sciences, and the liberal arts.
£138.70
John Wiley & Sons Inc Variance Components
Book SynopsisThis volume is written on the subject of the summarizing of the variability of statistical data known as the analysis of variance table. Penned in a readable style, it provides an up-to-date treatment of research in the area.Table of ContentsHistory and Comment. The 1-Way Classification. Balanced Data. Analysis of Variance Estimation for Unbalanced Data. Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML). Prediction of Random Variables. Computing ML and REML Estimates. Hierarchical Models and Bayesian Estimation. Binary and Discrete Data. Other Procedures. The Dispersion-Mean Model. Appendices. References. List of Tables and Figures. Indexes.
£108.86
John Wiley & Sons Inc Matrix Algebra Useful for Statistics
Book SynopsisWILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation.Table of Contents1. Introduction. 2. Basic Operations. 3. Special Matrices. 4. Determinants. 5. Inverse Matrices. 6. Rank. 7. Canonical Forms. 8. Generalized Inverses. 9. Solving Linear Equations. 10. Partitioned Matrices. 11. Eigenvalues and Eigenvectors. 11A. Appendix to Chapter 11. 12. Miscellanea. 13. Applications in Statistics. 14. The Matrix Algebra of Regression Analysis. 15. An Introduction to Linear Statistical Models. References. Index.
£115.16
John Wiley & Sons Inc Robust Statistics Theory and Methods 855 Wiley
Book SynopsisRobust Statistics fills the need for a solid, up-to-date text that presents a broad overview of the theory of robust statistics, integrated with applications and computing. The book features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series.Trade Review"This book belongs on the desk of every statistician working in robust statistics, and the authors are to be congratulated for providing the profession with a much-needed and valuable resource for teaching and research." (Journal of the American Statistical Association, June 2008) "…an original and valuable contribution…a source of inspiration for all those pursuing research in robust statistics." (Mathematical Reviews, 2007i) "…a great book for graduate students as well as for applied scientists and data analysts." (MAA Reviews, February 14, 2007)Table of ContentsPreface. 1. Introduction. 1.1 Classical and robust approaches to statistics. 1.2 Mean and standard deviation. 1.3 The “three-sigma edit” rule. 1.4 Linear regression. 1.5 Correlation coefficients. 1.6 Other parametric models. 1.7 Problems. 2. Location and Scale. 2.1 The location model. 2.2 M-estimates of location. 2.3 Trimmed means. 2.4 Dispersion estimates. 2.5 M-estimates of scale. 2.6 M-estimates of location with unknown dispersion. 2.7 Numerical computation of M-estimates. 2.8 Robust confidence intervals and tests. 2.9 Appendix: proofs and complements. 2.10 Problems. 3. Measuring Robustness. 3.1 The influence function. 3.2 The breakdown point. 3.3 Maximum asymptotic bias. 3.4 Balancing robustness and efficiency. 3.5 *“Optimal” robustness. 3.6 Multidimensional parameters. 3.7 *Estimates as functionals. 3.8 Appendix: proofs of results. 3.9 Problems. 4 Linear Regression 1. 4.1 Introduction. 4.2 Review of the LS method. 4.3 Classical methods for outlier detection. 4.4 Regression M-estimates. 4.5 Numerical computation of monotone M-estimates. 4.6 Breakdown point of monotone regression estimates. 4.7 Robust tests for linear hypothesis. 4.8 *Regression quantiles. 4.9 Appendix: proofs and complements. 4.10 Problems. 5 Linear Regression 2. 5.1 Introduction. 5.2 The linear model with random predictors 118 5.3 M-estimates with a bounded ρ-function. 5.4 Properties of M-estimates with a bounded ρ-function. 5.5 MM-estimates. 5.6 Estimates based on a robust residual scale. 5.7 Numerical computation of estimates based on robust scales. 5.8 Robust confidence intervals and tests for M-estimates. 5.9 Balancing robustness and efficiency. 5.10 The exact fit property. 5.11 Generalized M-estimates. 5.12 Selection of variables. 5.13 Heteroskedastic errors. 5.14 *Other estimates. 5.15 Models with numeric and categorical predictors. 5.16 *Appendix: proofs and complements. 5.17 Problems. 6. Multivariate Analysis. 6.1 Introduction. 6.2 Breakdown and efficiency of multivariate estimates. 6.3 M-estimates. 6.4 Estimates based on a robust scale. 6.5 The Stahel–Donoho estimate. 6.6 Asymptotic bias. 6.7 Numerical computation of multivariate estimates. 6.8 Comparing estimates. 6.9 Faster robust dispersion matrix estimates. 6.10 Robust principal components. 6.11 *Other estimates of location and dispersion. 6.12 Appendix: proofs and complements. 6.13 Problems. 7. Generalized Linear Models. 7.1 Logistic regression. 7.2 Robust estimates for the logistic model. 7.3 Generalized linear models. 7.4 Problems. 8. Time Series. 8.1 Time series outliers and their impact. 8.2 Classical estimates for AR models. 8.3 Classical estimates for ARMA models. 8.4 M-estimates of ARMA models. 8.5 Generalized M-estimates. 8.6 Robust AR estimation using robust filters. 8.7 Robust model identification. 8.8 Robust ARMA model estimation using robust filters. 8.9 ARIMA and SARIMA models. 8.10 Detecting time series outliers and level shifts. 8.11 Robustness measures for time series. 8.12 Other approaches for ARMA models. 8.13 High-efficiency robust location estimates. 8.14 Robust spectral density estimation. 8.15 Appendix A: heuristic derivation of the asymptotic distribution of M-estimates for ARMA models. 8.16 Appendix B: robust filter covariance recursions. 8.17 Appendix C: ARMA model state-space representation. 8.18 Problems. 9. Numerical Algorithms. 9.1 Regression M-estimates. 9.2 Regression S-estimates. 9.3 The LTS-estimate. 9.4 Scale M-estimates. 9.5 Multivariate M-estimates. 9.6 Multivariate S-estimates. 10. Asymptotic Theory of M-estimates. 10.1 Existence and uniqueness of solutions. 10.2 Consistency. 10.3 Asymptotic normality. 10.4 Convergence of the SC to the IF. 10.5 M-estimates of several parameters. 10.6 Location M-estimates with preliminary scale. 10.7 Trimmed means. 10.8 Optimality of the MLE. 10.9 Regression M-estimates. 10.10 Nonexistence of moments of the sample median. 10.11 Problems. 11. Robust Methods in S-Plus. 11.1 Location M-estimates: function Mestimate. 11.2 Robust regression. 11.3 Robust dispersion matrices. 11.4 Principal components. 11.5 Generalized linear models. 11.6 Time series. 11.7 Public-domain software for robust methods. 12. Description of Data Sets. Bibliography. Index.
£78.26
John Wiley & Sons Inc Statistical Analysis and Modelling From Spatial
Book SynopsisStatistical Analysis and Modelling of Spatial Point Patterns provides an accessible account of the statistical analysis of spatial point patterns taking particular account of spatial data. Applications are central to the book and there are examples from biology, geology, ecology and environmental sciences as well as forestry.Trade Review"It adopts an extremely accessible style, allowing the non-statistician complete understanding, describes the process of extracting knowledge from the data, emphasizing marked point processes, demonstrates the analysis of complex data sets, using applied examples from areas including biology, forestry, and materials science, and features a supplementary website containing example datasets. This text is ideally suited for researchers in many areas of applications, including environmental statistics, ecology, physics, material science, geostatistics, and biology. It is also suitable for students of statistics, mathematics, computer science, biology and geoinformatics." (Zentralblatt Math, 2010) "Statistical Analysis and Modelling of Spatial Point Patterns is an extremely well-written book and is accessible to a wide audience, including both applied statisticians and researchers from other fields with a reasonably sophisticated background in statics." (Journal of the American Statistical Association, September 2010)“The book presents statistical methods that are relevant in practice, focusing on traditional methods, in particular those based on summary statistics, but also more recent models and methods are briefly discussed. ”(Biometrics , September 2009) "The book is a useful addition to Wiley's series Statistics in Practice." (Journal of Tropical Pediatrics, February 2009) "The abstract flavor this brings to the subject means that methods may have very wide applicability over different application domains. This applicability, in turn, is reflected by the large number of interesting examples described in the book. The book provides a comprehensive overview of the area." (International Statistical Review, December 2008)Table of ContentsPreface. List of Examples. 1. Introduction. 1.1 Point process statistics. 1.2 Examples of point process data. 1.2.1 A pattern of amacrine cells. 1.2.2 Gold particles. 1.2.3 A pattern of Western Australian plants. 1.2.4 Waterstriders. 1.2.5 A sample of concrete. 1.3 Historical notes. 1.3.1 Determination of number of trees in a forest. 1.3.2 Number of blood particles in a sample. 1.3.3 Patterns of points in plant communities. 1.3.4 Formulating the power law for the pair correlation function for galaxies. 1.4 Sampling and data collection. 1.4.1 General remarks. 1.4.2 Choosing an appropriate study area. 1.4.3 Data collection. 1.5 Fundamentals of the theory of point processes. 1.6 Stationarity and isotropy. 1.6.1 Model approach and design approach. 1.6.2 Finite and infinite point processes. 1.6.3 Stationarity and isotropy. 1.6.4 Ergodicity. 1.7 Summary characteristics for point processes. 1.7.1 Numerical summary characteristics. 1.7.2 Functional summary characteristics. 1.8 Secondary structures of point processes. 1.8.1 Introduction. 1.8.2 Random sets. 1.8.3 Random fields. 1.8.4 Tessellations. 1.8.5 Neighbour networks or graphs. 1.9 Simulation of point processes. 2. The Homogeneous Poisson point process. 2.1 Introduction. 2.2 The binomial point process. 2.2.1 Introduction. 2.2.2 Basic properties. 2.2.3 The periodic binomial process. 2.2.4 Simulation of the binomial process. 2.3 The homogeneous Poisson point process. 2.3.1 Introduction. 2.3.2 Basic properties. 2.3.3 Characterisations of the homogeneous Poisson process. 2.4 Simulation of a homogeneous Poisson process. 2.5 Model characteristics. 2.5.1 Moments and moment measures. 2.5.2 The Palm distribution of a homogeneous Poisson process. 2.5.3 Summary characteristics of the homogeneous Poisson process. 2.6 Estimating the intensity. 2.7 Testing complete spatial randomness. 2.7.1 Introduction. 2.7.2 Quadrat counts. 2.7.3 Distance methods. 2.7.4 The J-test. 2.7.5 Two index-based tests. 2.7.6 Discrepancy tests. 2.7.7 The L-test. 2.7.8 Other tests and recommendations. 3. Finite point processes. 3.1 Introduction. 3.2 Distributions of numbers of points. 3.2.1 The binomial distribution. 3.2.2 The Poisson distribution. 3.2.3 Compound distributions. 3.2.4 Generalised distributions. 3.3 Intensity functions and their estimation. 3.3.1 Parametric statistics for the intensity function. 3.3.2 Non-parametric estimation of the intensity function. 3.3.3 Estimating the point density distribution function. 3.4 Inhomogeneous Poisson process and finite Cox process. 3.4.1 The inhomogeneous Poisson process. 3.4.2 The finite Cox process. 3.5 Summary characteristics for finite point processes. 3.5.1 Nearest-neighbour distances. 3.5.2 Dilation function. 3.5.3 Graph-theoretic statistics. 3.5.4 Second-order characteristics. 3.6 Finite Gibbs processes. 3.6.1 Introduction. 3.6.2 Gibbs processes with fixed number of points. 3.6.3 Gibbs processes with a random number of points. 3.6.4 Second-order summary characteristics of finite Gibbs processes. 3.6.5 Further discussion. 3.6.6 Statistical inference for finite Gibbs processes. 4. Stationary point processes. 4.1 Basic definitions and notation. 4.2 Summary characteristics for stationary point processes. 4.2.1 Introduction. 4.2.2 Edge-correction methods. 4.2.3 The intensity λ. 4.2.4 Indices as summary characteristics. 4.2.5 Empty-space statistics and other morphological summaries. 4.2.6 The nearest-neighbour distance distribution function. 4.2.7 The J-function. 4.3 Second-order characteristics. 4.3.1 The three functions: K, L and g. 4.3.2 Theoretical foundations of second-order characteristics. 4.3.3 Estimators of the second-order characteristics. 4.3.4 Interpretation of pair correlation functions. 4.4 Higher-order and topological characteristics. 4.4.1 Introduction. 4.4.2 Third-order characteristics. 4.4.3 Delaunay tessellation characteristics. 4.4.4 The connectivity function. 4.5 Orientation analysis for stationary point processes. 4.5.1 Introduction. 4.5.2 Nearest-neighbour orientation distribution. 4.5.3 Second-order orientation analysis. 4.6 Outliers, gaps and residuals. 4.6.1 Introduction. 4.6.2 Simple outlier detection. 4.6.3 Simple gap detection. 4.6.4 Model-based outliers. 4.6.5 Residuals. 4.7 Replicated patterns. 4.7.1 Introduction. 4.7.2 Aggregation recipes. 4.8 Choosing appropriate observation windows. 4.8.1 General ideas. 4.8.2 Representative windows. 4.9 Multivariate analysis of series of point patterns. 4.10 Summary characteristics for the non-stationary case. 4.10.1 Formal application of stationary characteristics and estimators. 4.10.2 Intensity reweighting. 4.10.3 Local rescaling. 5. Stationary marked point processes. 5.1 Basic definitions and notation. 5.1.1 Introduction. 5.1.2 Marks and their properties. 5.1.3 Marking models. 5.1.4 Stationarity. 5.1.5 First-order characteristics. 5.1.6 Mark-sum measure. 5.1.7 Palm distribution. 5.2 Summary characteristics. 5.2.1 Introduction. 5.2.2 Intensity and mark-sum intensity. 5.2.3 Mean mark, mark d.f. and mark probabilities. 5.2.4 Indices for stationary marked point processes. 5.2.5 Nearest-neighbour distributions. 5.3 Second-order characteristics for marked point processes. 5.3.1 Introduction. 5.3.2 Definitions for qualitative marks. 5.3.3 Definitions for quantitative marks. 5.3.4 Estimation of second-order characteristics. 5.4 Orientation analysis for marked point processes. 5.4.1 Introduction. 5.4.2 Orientation analysis for non-isotropic processes with angular marks. 5.4.3 Orientation analysis for isotropic processes with angular marks. 5.4.4 Orientation analysis with constructed marks. 6. Modelling and simulation of stationary point processes. 6.1 Introduction. 6.2 Operations with point processes. 6.2.1 Thinning. 6.2.2 Clustering. 6.2.3 Superposition. 6.3 Cluster processes. 6.3.1 General cluster processes. 6.3.2 Neyman-Scott processes. 6.4 Stationary Cox processes. 6.4.1 Introduction. 6.4.2 Properties of stationary Cox processes. 6.5 Hard-core point processes. 6.5.1 Introduction. 6.5.2 Matérn hard-core processes. 6.5.3 The dead leaves model. 6.5.4 The RSA model. 6.5.5 Random dense packings of hard spheres. 6.6 Stationary Gibbs processes. 6.6.1 Basic ideas and equations. 6.6.2 Simulation of stationary Gibbs processes. 6.6.3 Statistics for stationary Gibbs processes. 6.7 Reconstruction of point patterns. 6.7.1 Reconstructing point patterns without a specified model. 6.7.2 An example: reconstruction of Neyman-Scott processes. 6.7.3 Practical application of the reconstruction algorithm. 6.8 Formulas for marked point process models. 6.8.1 Introduction. 6.8.2 Independent marks. 6.8.3 Random field model. 6.8.4 Intensity-weighted marks. 6.9 Moment formulas for stationary shot-noise fields. 6.10 Space-time point processes. 6.10.1 Introduction. 6.10.2 Space-time Poisson processes. 6.10.3 Second-order statistics for completely stationary event processes. 6.10.4 Two examples of space-time processes. 6.11 Correlations between point processes and other random structures. 6.11.1 Introduction. 6.11.2 Correlations between point processes and random fields. 6.11.3 Correlations between point processes and fibre processes. 7. Fitting and testing point process models. 7.1 Choice of model. 7.2 Parameter estimation. 7.2.1 Maximum likelihood method. 7.2.2 Method of moments. 7.2.3 Trial-and-error estimation. 7.3 Variance estimation by bootstrap. 7.4 Goodness-of-fit tests. 7.4.1 Envelope test. 7.4.2 Deviation test. 7.5 Testing mark hypotheses. 7.5.1 Introduction. 7.5.2 Testing independent marking, test of association. 7.5.3 Testing geostatistical marking. 7.6 Bayesian methods for point pattern analysis. Appendix A Fundamentals of statistics. Appendix B Geometrical characteristics of sets. Appendix C Fundamentals of geostatistics. References. Notation index. Author index. Subject index.
£98.96
John Wiley & Sons Inc Large Deviations for Gaussian Modelling
Book SynopsisThis book describes how modern queuing theory can be applied to problems in telecommunication engineering. It starts with a survey of the essential theory behind Gaussian processes, large deviations, and queuing theory and then introduces the idea of a traffic processes in communication systems.Trade Review"The book maybe useful for specialists connected with queuing theory and working in applied probability." (Zentralblatt MATH, 2008)Table of ContentsPreface and acknowledgments. 1 Introduction. Part A: Gaussian traffic and large deviations. 2 The Gaussian source model. 2.1 Modeling network traffic. 2.2 Notation and preliminaries on Gaussian random variables. 2.3 Gaussian sources. 2.4 Generic examples-long-range dependence and smoothness. 2.5 Other useful Gaussian source models. 2.6 Applicability of Gaussian source models for network traffic. 3 Gaussian sources: validation, justification. 3.1 Validation. 3.2 Convergence of on-off traffic to a Gaussian process. 4 Large deviations for Gaussian processes. 4.1 Cram´er's theorem. 4.2 Schilder's theorem. Part B: Large deviations of Gaussian queues. 5 Gaussian queues: an introduction. 5.1 Lindley's recursion, the steady-state buffer content. 5.2 Gaussian queues. 5.3 Special cases: Brownian motion and Brownian bridge. 5.4 A powerful approximation. 5.5 Asymptotics. 5.6 Large-buffer asymptotics. 6 Logarithmic many-sources asymptotics. 6.1 Many-sources asymptotics: the loss curve. 6.2 Duality between loss curve and variance function. 6.3 The buffer-bandwidth curve is convex. 7 Exact many-sources asymptotics. 7.1 Slotted time: results. 7.2 Slotted time: proofs. 7.3 Continuous time: results. 7.4 Continuous time: proofs. 8 Simulation. 8.1 Determining the simulation horizon. 8.2 Importance sampling algorithms. 8.3 Asymptotic efficiency. 8.4 Efficient estimation of the overflow probability. 9 Tandem and priority queues. 9.1 Tandem: model and preliminaries. 9.2 Tandem: lower bound on the decay rate. 9.3 Tandem: tightness of the decay rate. 9.4 Tandem: properties of the input rate path. 9.5 Tandem: examples. 9.6 Priority queues. 10 Generalized processor sharing. 10.1 Preliminaries on GPS. 10.2 Generic upper and lower bound on the overflow probability. 10.3 Lower bound on the decay rate: class 2 in underload. 10.4 Upper bound on the decay rate: class 2 in underload. 10.5 Analysis of the decay rate: class 2 in overload. 10.6 Discussion of the results. 10.7 Delay asymptotics. 11 Explicit results for short-range dependent inputs. 11.1 Asymptotically linear variance; some preliminaries. 11.2 Tandem queue with srd input. 11.3 Priority queue with srd input. 11.4 GPS queue with srd input. 11.5 Concluding remarks. 12 Brownian queues. 12.1 Single queue: detailed results. 12.2 Tandem: distribution of the downstream queue. 12.3 Tandem: joint distribution. Part C: Applications. 13 Weight setting in GPS. 13.1 An optimal partitioning approach to weight setting. 13.2 Approximation of the overflow probabilities. 13.3 Fixed weights. 13.4 Realizable region. 14 A link dimensioning formula and empirical support. 14.1 Objectives, modeling, and analysis. 14.2 Numerical study. 14.3 Empirical study. 14.4 Implementation aspects. 15 Link dimensioning: indirect variance estimation. 15.1 Theoretical foundations. 15.2 Implementation issues. 15.3 Error analysis of the inversion procedure. 15.4 Validation. 16 A framework for bandwidth trading. 16.1 Bandwidth trading. 16.2 Model and preliminaries. 16.3 Single-link network. 16.4 Gaussian traffic; utility as a function of loss. 16.5 Sanov's theorem and its inverse. 16.6 Estimation of loss probabilities. 16.7 Numerical example. Bibliography. Index.
£101.66
John Wiley & Sons Inc LQ Dynamic Optimization and Differential Games
Book SynopsisLinear Quadratic Differential Games is an assessment of the state of the art in its field and modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management.Table of ContentsPreface. Notation and symbols. 1 Introduction. 1.1 Historical perspective. 1.2 How to use this book. 1.3 Outline of this book. 1.4 Notes and references. 2 Linear algebra. 2.1 Basic concepts in linear algebra. 2.2 Eigenvalues and eigenvectors. 2.3 Complex eigenvalues. 2.4 Cayley–Hamilton theorem. 2.5 Invariant subspaces and Jordan canonical form. 2.6 Semi-definite matrices. 2.7 Algebraic Riccati equations. 2.8 Notes and references. 2.9 Exercises. 2.10 Appendix. 3 Dynamical systems. 3.1 Description of linear dynamical systems. 3.2 Existence–uniqueness results for differential equations. 3.2.1 General case. 3.2.2 Control theoretic extensions. 3.3 Stability theory: general case. 3.4 Stability theory of planar systems. 3.5 Geometric concepts. 3.6 Performance specifications. 3.7 Examples of differential games. 3.8 Information, commitment and strategies. 3.9 Notes and references. 3.10 Exercises. 3.11 Appendix. 4 Optimization techniques. 4.1 Optimization of functions. 4.2 The Euler–Lagrange equation. 4.3 Pontryagin’s maximum principle. 4.4 Dynamic programming principle. 4.5 Solving optimal control problems. 4.6 Notes and references. 4.7 Exercises. 4.8 Appendix. 5 Regular linear quadratic optimal control. 5.1 Problem statement. 5.2 Finite-planning horizon. 5.3 Riccati differential equations. 5.4 Infinite-planning horizon. 5.5 Convergence results. 5.6 Notes and references. 5.7 Exercises. 5.8 Appendix. 6 Cooperative games. 6.1 Pareto solutions. 6.2 Bargaining concepts. 6.3 Nash bargaining solution. 6.4 Numerical solution. 6.5 Notes and references. 6.6 Exercises. 6.7 Appendix. 7 Non-cooperative open-loop information games. 7.1 Introduction. 7.2 Finite-planning horizon. 7.3 Open-loop Nash algebraic Riccati equations. 7.4 Infinite-planning horizon. 7.5 Computational aspects and illustrative examples. 7.6 Convergence results. 7.7 Scalar case. 7.8 Economics examples. 7.8.1 A simple government debt stabilization game. 7.8.2 A game on dynamic duopolistic competition. 7.9 Notes and references. 7.10 Exercises. 7.11 Appendix. 8 Non-cooperative feedback information games. 8.1 Introduction. 8.2 Finite-planning horizon. 8.3 Infinite-planning horizon. 8.4 Two-player scalar case. 8.5 Computational aspects. 8.5.1 Preliminaries. 8.5.2 A scalar numerical algorithm: the two-player case. 8.5.3 The N-player scalar case. 8.6 Convergence results for the two-player scalar case. 8.7 Notes and references. 8.8 Exercises. 8.9 Appendix. 9 Uncertain non-cooperative feedback information games. 9.1 Stochastic approach. 9.2 Deterministic approach: introduction. 9.3 The one-player case. 9.4 The one-player scalar case. 9.5 The two-player case. 9.6 A fishery management game. 9.7 A scalar numerical algorithm. 9.8 Stochastic interpretation. 9.9 Notes and references. 9.10 Exercises. 9.11 Appendix. References. Index.
£101.66
John Wiley & Sons Inc Theoretical Foundations of Functional Data
Book Synopsis?? Provides a concise but rigorous account of the theoretical background of FDA. ?? Introduces topics in various areas of mathematics, probability and statistics from the perspective of FDA. ?? Presents a systematic exposition of the fundamental statistical issues in FDA.Table of ContentsPreface xi 1 Introduction 1 1.1 Multivariate analysis in a nutshell 2 1.2 The path that lies ahead 13 2 Vector and function spaces 15 2.1 Metric spaces 16 2.2 Vector and normed spaces 20 2.3 Banach and Lp spaces 26 2.4 Inner Product and Hilbert spaces 31 2.5 The projection theorem and orthogonal decomposition 38 2.6 Vector integrals 40 2.7 Reproducing kernel Hilbert spaces 46 2.8 Sobolev spaces 55 3 Linear operator and functionals 61 3.1 Operators 62 3.2 Linear functionals 66 3.3 Adjoint operator 71 3.4 Nonnegative, square-root, and projection operators 74 3.5 Operator inverses 77 3.6 Fréchet and Gâteaux derivatives 83 3.7 Generalized Gram–Schmidt decompositions 87 4 Compact operators and singular value decomposition 91 4.1 Compact operators 92 4.2 Eigenvalues of compact operators 96 4.3 The singular value decomposition 103 4.4 Hilbert–Schmidt operators 107 4.5 Trace class operators 113 4.6 Integral operators and Mercer’s Theorem 116 4.7 Operators on an RKHS 123 4.8 Simultaneous diagonalization of two nonnegative definite operators 126 5 Perturbation theory 129 5.1 Perturbation of self-adjoint compact operators 129 5.2 Perturbation of general compact operators 140 6 Smoothing and regularization 147 6.1 Functional linear model 147 6.2 Penalized least squares estimators 150 6.3 Bias and variance 157 6.4 A computational formula 158 6.5 Regularization parameter selection 161 6.6 Splines 165 7 Random elements in a Hilbert space 175 7.1 Probability measures on a Hilbert space 176 7.2 Mean and covariance of a random element of a Hilbert space 178 7.3 Mean-square continuous processes and the Karhunen–Lòeve Theorem 184 7.4 Mean-square continuous processes in L2 (E,B(E), mu) 190 7.5 RKHS valued processes 195 7.6 The closed span of a process 198 7.7 Large sample theory 203 8 Mean and covariance estimation 211 8.1 Sample mean and covariance operator 212 8.2 Local linear estimation 214 8.3 Penalized least-squares estimation 231 9 Principal components analysis 251 9.1 Estimation via the sample covariance operator 253 9.2 Estimation via local linear smoothing 255 9.3 Estimation via penalized least squares 261 10 Canonical correlation analysis 265 10.1 CCA for random elements of a Hilbert space 267 10.2 Estimation 274 10.3 Prediction and regression 281 10.4 Factor analysis 284 10.5 MANOVA and discriminant analysis 288 10.6 Orthogonal subspaces and partial cca 294 11 Regression 305 11.1 A functional regression model 305 11.2 Asymptotic theory 308 11.3 Minimax optimality 318 11.4 Discretely sampled data 321 References 327 Index 331 Notation Index 334
£62.65
John Wiley & Sons Inc Bayesian Biostatistics
Book Synopsis* This book provides an authoritative account of Bayesian methodology, from its most basic elements to its practical implementations, with an emphasis on healthcare techniques. * Contains introductory explanations of Bayesian principles common to all areas.Trade Review“In conclusion, we consider the book by Lesaffre and Lawson a noteworthy contribution to the dissemination of Bayesian methods, and a good manual of reference for many common and some specialized applications in biomedical research. The great variety of examples and topics covered offers both advantages and disadvantages. Some parts might be too specialized for statistics students, but lecturers and applied statisticians will benefit a lot from the authors’ wealth of experience.” (Biometrical Journal, 15 July 2013) “The book Bayesian Biostatisticsby Lesaffre and Lawson, is a welcoming addition to this important area of research in biostatistical applications. For example, in the area of clinical trials, Bayesian methods provide flexibility and benefits for incorporating historical data with current data and then using the resulting posterior to make probability statements for different outcomes”.(Journal of Biopharmaceutical Statistics, 1 January 2013) Table of ContentsPreface xiii Notation, terminology and some guidance for reading the book xvii Part I Basic Concepts in Bayesian Methods 1 Modes of statistical inference 3 1.1 The frequentist approach: A critical reflection 4 1.1.1 The classical statistical approach 4 1.1.2 The P-value as a measure of evidence 5 1.1.3 The confidence interval as a measure of evidence 8 1.1.4 An historical note on the two frequentist paradigms∗ 8 1.2 Statistical inference based on the likelihood function 10 1.2.1 The likelihood function 10 1.2.2 The likelihood principles 11 1.3 The Bayesian approach: Some basic ideas 14 1.3.1 Introduction 14 1.3.2 Bayes theorem – discrete version for simple events 15 1.4 Outlook 18 Exercises 19 2 Bayes theorem: Computing the posterior distribution 20 2.1 Introduction 20 2.2 Bayes theorem – the binary version 20 2.3 Probability in a Bayesian context 21 2.4 Bayes theorem – the categorical version 22 2.5 Bayes theorem – the continuous version 23 2.6 The binomial case 24 2.7 The Gaussian case 30 2.8 The Poisson case 36 2.9 The prior and posterior distribution of h(θ) 40 2.10 Bayesian versus likelihood approach 40 2.11 Bayesian versus frequentist approach 41 2.12 The different modes of the Bayesian approach 41 2.13 An historical note on the Bayesian approach 42 2.14 Closing remarks 44 Exercises 44 3 Introduction to Bayesian inference 46 3.1 Introduction 46 3.2 Summarizing the posterior by probabilities 46 3.3 Posterior summary measures 47 3.3.1 Characterizing the location and variability of the posterior distribution 47 3.3.2 Posterior interval estimation 49 3.4 Predictive distributions 51 3.4.1 The frequentist approach to prediction 52 3.4.2 The Bayesian approach to prediction 53 3.4.3 Applications 54 3.5 Exchangeability 58 3.6 A normal approximation to the posterior 60 3.6.1 A Bayesian analysis based on a normal approximation to the likelihood 60 3.6.2 Asymptotic properties of the posterior distribution 62 3.7 Numerical techniques to determine the posterior 63 3.7.1 Numerical integration 63 3.7.2 Sampling from the posterior 65 3.7.3 Choice of posterior summary measures 72 3.8 Bayesian hypothesis testing 72 3.8.1 Inference based on credible intervals 72 3.8.2 The Bayes factor 74 3.8.3 Bayesian versus frequentist hypothesis testing 76 3.9 Closing remarks 78 Exercises 79 4 More than one parameter 82 4.1 Introduction 82 4.2 Joint versus marginal posterior inference 83 4.3 The normal distribution with μ and σ2 unknown 83 4.3.1 No prior knowledge on μ and σ2 is available 84 4.3.2 An historical study is available 86 4.3.3 Expert knowledge is available 88 4.4 Multivariate distributions 89 4.4.1 The multivariate normal and related distributions 89 4.4.2 The multinomial distribution 90 4.5 Frequentist properties of Bayesian inference 92 4.6 Sampling from the posterior distribution: The Method of Composition 93 4.7 Bayesian linear regression models 96 4.7.1 The frequentist approach to linear regression 96 4.7.2 A noninformative Bayesian linear regression model 97 4.7.3 Posterior summary measures for the linear regression model 98 4.7.4 Sampling from the posterior distribution 99 4.7.5 An informative Bayesian linear regression model 101 4.8 Bayesian generalized linear models 101 4.9 More complex regression models 102 4.10 Closing remarks 102 Exercises 102 5 Choosing the prior distribution 104 5.1 Introduction 104 5.2 The sequential use of Bayes theorem 104 5.3 Conjugate prior distributions 106 5.3.1 Univariate data distributions 106 5.3.2 Normal distribution – mean and variance unknown 109 5.3.3 Multivariate data distributions 110 5.3.4 Conditional conjugate and semiconjugate distributions 111 5.3.5 Hyperpriors 112 5.4 Noninformative prior distributions 113 5.4.1 Introduction 113 5.4.2 Expressing ignorance 114 5.4.3 General principles to choose noninformative priors 115 5.4.4 Improper prior distributions 119 5.4.5 Weak/vague priors 120 5.5 Informative prior distributions 121 5.5.1 Introduction 121 5.5.2 Data-based prior distributions 121 5.5.3 Elicitation of prior knowledge 122 5.5.4 Archetypal prior distributions 126 5.6 Prior distributions for regression models 129 5.6.1 Normal linear regression 129 5.6.2 Generalized linear models 131 5.6.3 Specification of priors in Bayesian software 134 5.7 Modeling priors 134 5.8 Other regression models 136 5.9 Closing remarks 136 Exercises 137 6 Markov chain Monte Carlo sampling 139 6.1 Introduction 139 6.2 The Gibbs sampler 140 6.2.1 The bivariate Gibbs sampler 140 6.2.2 The general Gibbs sampler 146 6.2.3 Remarks∗ 150 6.2.4 Review of Gibbs sampling approaches 152 6.2.5 The Slice sampler∗ 153 6.3 The Metropolis(–Hastings) algorithm 154 6.3.1 The Metropolis algorithm 155 6.3.2 The Metropolis–Hastings algorithm 157 6.3.3 Remarks∗ 159 6.3.4 Review of Metropolis(–Hastings) approaches 161 6.4 Justification of the MCMC approaches∗ 162 6.4.1 Properties of the MH algorithm 164 6.4.2 Properties of the Gibbs sampler 165 6.5 Choice of the sampler 165 6.6 The Reversible Jump MCMC algorithm∗ 168 6.7 Closing remarks 172 Exercises 173 7 Assessing and improving convergence of the Markov chain 175 7.1 Introduction 175 7.2 Assessing convergence of a Markov chain 176 7.2.1 Definition of convergence for a Markov chain 176 7.2.2 Checking convergence of the Markov chain 176 7.2.3 Graphical approaches to assess convergence 177 7.2.4 Formal diagnostic tests 180 7.2.5 Computing the Monte Carlo standard error 186 7.2.6 Practical experience with the formal diagnostic procedures 188 7.3 Accelerating convergence 189 7.3.1 Introduction 189 7.3.2 Acceleration techniques 189 7.4 Practical guidelines for assessing and accelerating convergence 194 7.5 Data augmentation 195 7.6 Closing remarks 200 Exercises 201 8 Software 202 8.1 WinBUGS and related software 202 8.1.1 A first analysis 203 8.1.2 Information on samplers 206 8.1.3 Assessing and accelerating convergence 207 8.1.4 Vector and matrix manipulations 208 8.1.5 Working in batch mode 210 8.1.6 Troubleshooting 212 8.1.7 Directed acyclic graphs 212 8.1.8 Add-on modules: GeoBUGS and PKBUGS 214 8.1.9 Related software 214 8.2 Bayesian analysis using SAS 215 8.2.1 Analysis using procedure GENMOD 215 8.2.2 Analysis using procedure MCMC 217 8.2.3 Other Bayesian programs 220 8.3 Additional Bayesian software and comparisons 221 8.3.1 Additional Bayesian software 221 8.3.2 Comparison of Bayesian software 222 8.4 Closing remarks 222 Exercises 223 Part II Bayesian Tools for Statistical Modeling 9 Hierarchical models 227 9.1 Introduction 227 9.2 The Poisson-gamma hierarchical model 228 9.2.1 Introduction 228 9.2.2 Model specification 229 9.2.3 Posterior distributions 231 9.2.4 Estimating the parameters 232 9.2.5 Posterior predictive distributions 237 9.3 Full versus empirical Bayesian approach 238 9.4 Gaussian hierarchical models 240 9.4.1 Introduction 240 9.4.2 The Gaussian hierarchical model 240 9.4.3 Estimating the parameters 241 9.4.4 Posterior predictive distributions 243 9.4.5 Comparison of FB and EB approach 244 9.5 Mixed models 244 9.5.1 Introduction 244 9.5.2 The linear mixed model 244 9.5.3 The generalized linear mixed model 248 9.5.4 Nonlinear mixed models 253 9.5.5 Some further extensions 256 9.5.6 Estimation of the random effects and posterior predictive distributions 256 9.5.7 Choice of the level-2 variance prior 258 9.6 Propriety of the posterior 260 9.7 Assessing and accelerating convergence 261 9.8 Comparison of Bayesian and frequentist hierarchical models 263 9.8.1 Estimating the level-2 variance 263 9.8.2 ML and REml estimates compared with Bayesian estimates 264 9.9 Closing remarks 265 Exercises 265 10 Model building and assessment 267 10.1 Introduction 267 10.2 Measures for model selection 268 10.2.1 The Bayes factor 268 10.2.2 Information theoretic measures for model selection 274 10.2.3 Model selection based on predictive loss functions 286 10.3 Model checking 288 10.3.1 Introduction 288 10.3.2 Model-checking procedures 289 10.3.3 Sensitivity analysis 295 10.3.4 Posterior predictive checks 300 10.3.5 Model expansion 308 10.4 Closing remarks 316 Exercises 316 11 Variable selection 319 11.1 Introduction 319 11.2 Classical variable selection 320 11.2.1 Variable selection techniques 320 11.2.2 Frequentist regularization 322 11.3 Bayesian variable selection: Concepts and questions 325 11.4 Introduction to Bayesian variable selection 326 11.4.1 Variable selection for K small 326 11.4.2 Variable selection for K large 330 11.5 Variable selection based on Zellner’s g-prior 333 11.6 Variable selection based on Reversible Jump Markov chain Monte Carlo 336 11.7 Spike and slab priors 339 11.7.1 Stochastic Search Variable Selection 340 11.7.2 Gibbs Variable Selection 343 11.7.3 Dependent variable selection using SSVS 345 11.8 Bayesian regularization 345 11.8.1 Bayesian LASSO regression 346 11.8.2 Elastic Net and further extensions of the Bayesian LASSO 350 11.9 The many regressors case 351 11.10 Bayesian model selection 355 11.11 Bayesian model averaging 357 11.12 Closing remarks 359 Exercises 360 Part III Bayesian Methods in Practical Applications 12 Bioassay 365 12.1 Bioassay essentials 365 12.1.1 Cell assays 365 12.1.2 Animal assays 366 12.2 A generic in vitro example 369 12.3 Ames/Salmonella mutagenic assay 371 12.4 Mouse lymphoma assay (L5178Y TK+/−) 373 12.5 Closing remarks 374 13 Measurement error 375 13.1 Continuous measurement error 375 13.1.1 Measurement error in a variable 375 13.1.2 Two types of measurement error on the predictor in linear and nonlinear models 376 13.1.3 Accommodation of predictor measurement error 378 13.1.4 Nonadditive errors and other extensions 382 13.2 Discrete measurement error 382 13.2.1 Sources of misclassification 382 13.2.2 Misclassification in the binary predictor 383 13.2.3 Misclassification in a binary response 386 13.3 Closing remarks 389 14 Survival analysis 390 14.1 Basic terminology 390 14.1.1 Endpoint distributions 391 14.1.2 Censoring 392 14.1.3 Random effect specification 393 14.1.4 A general hazard model 393 14.1.5 Proportional hazards 394 14.1.6 The Cox model with random effects 394 14.2 The Bayesian model formulation 394 14.2.1 A Weibull survival model 395 14.2.2 A Bayesian AFT model 397 14.3 Examples 397 14.3.1 The gastric cancer study 397 14.3.2 Prostate cancer in Louisiana: A spatial AFT model 401 14.4 Closing remarks 406 15 Longitudinal analysis 407 15.1 Fixed time periods 407 15.1.1 Introduction 407 15.1.2 A classical growth-curve example 408 15.1.3 Alternate data models 414 15.2 Random event times 417 15.3 Dealing with missing data 420 15.3.1 Introduction 420 15.3.2 Response missingness 421 15.3.3 Missingness mechanisms 422 15.3.4 Bayesian considerations 424 15.3.5 Predictor missingness 424 15.4 Joint modeling of longitudinal and survival responses 424 15.4.1 Introduction 424 15.4.2 An example 425 15.5 Closing remarks 429 16 Spatial applications: Disease mapping and image analysis 430 16.1 Introduction 430 16.2 Disease mapping 430 16.2.1 Some general spatial epidemiological issues 431 16.2.2 Some spatial statistical issues 433 16.2.3 Count data models 433 16.2.4 A special application area: Disease mapping/risk estimation 434 16.2.5 A special application area: Disease clustering 438 16.2.6 A special application area: Ecological analysis 443 16.3 Image analysis 444 16.3.1 fMRI modeling 446 16.3.2 A note on software 455 17 Final chapter 456 17.1 What this book covered 456 17.2 Additional Bayesian developments 456 17.2.1 Medical decision making 456 17.2.2 Clinical trials 457 17.2.3 Bayesian networks 457 17.2.4 Bioinformatics 458 17.2.5 Missing data 458 17.2.6 Mixture models 458 17.2.7 Nonparametric Bayesian methods 459 17.3 Alternative reading 459 Appendix: Distributions 460 A.1 Introduction 460 A.2 Continuous univariate distributions 461 A.3 Discrete univariate distributions 477 A.4 Multivariate distributions 481 References 484 Index 509
£53.15
John Wiley & Sons Inc Methodology of Longitudinal Surveys
Book SynopsisThis book describes in detail the design, implementation and analysis of longitudinal surveys. Focusing primarily on surveys that involve collecting data from subjects on multiple occasions, it also covers issues that arise in surveys that collect longitudinal data via retrospective methods and ethical issues, including confidentiality and consent.Trade Review“This text is a ‘‘must’’ on the bookshelves of those of us who are engaged day to day in designing, conducting, or analyzing longitudinal survey data.” (Public Opinion Quarterly, 14 February 2012) “This text is a ‘‘must’’ on the bookshelves of those of us who are engaged day to day in designing, conducting, or analyzing longitudinal survey data.” (Public Opinion Quarterly, 22 March 2012)Table of ContentsPreface. 1. Methods for Longitudinal Surveys (Peter Lynn). 1.1 Introduction,. 1.2 Types of Longitudinal Surveys,. 1.3 Strengths of Longitudinal Surveys. 1.4 Weaknesses of Longitudinal Surveys. 1.5 Design Features Specific to Longitudinal Surveys. 1.6 Quality in Longitudinal Surveys. 1.7 Conclusions. References. 2. Sample Design for Longitudinal Surveys (Paul Smith, Peter Lynn and Dave Elliot). 2.1 Introduction. 2.2 Types of Longitudinal Sample Design. 2.3 Fundamental Aspects of Sample Design. 2.4 Other Aspects of Design and Implementation. 2.5 Conclusion. References. 3. Ethical Issues in Longitudinal Surveys (Carli Lessof). 3.1 Introduction. 3.2 History of Research Ethics. 3.3 Informed Consent. 3.4 Free Choice Regarding Participation. 3.5 Avoiding Harm. 3.6 Participant Confidentiality and Data Protection. 3.7 Independent Ethical Overview and Participant Involvement. Acknowledgements. References. 4. Enhancing Longitudinal Surveys by Linking to Administrative Data (Lisa Calderwood and Carli Lessof). 4.1 Introduction. 4.2 Administrative Data as a Research Resource. 4.3 Record Linkage Methodology. 4.4 Linking Survey Data with Administrative Data at Individual Level. 4.5 Ethical and Legal Issues. 4.6 Conclusion. References. 5. Tackling Seam Bias Through Questionnaire Design (Jeffrey Moore, Nancy Bates, Joanne Pascale and Aniekan Okon). 5.1 Introduction. 5.2 Previous Research on Seam Bias. 5.3 SIPP and its Dependent Interviewing Procedures. 5.4 Seam Bias Comparison - SIPP 2001 and SIPP 2004. 5.5 Conclusions and Discussion. References. 6. Dependent Interviewing: A Framework and Application. to Current Research (Annette Jäckle). 6.1 Introduction. 6.2 Dependent Interviewing - What and Why? 6.3 Design Options and their Effects. 6.4 Empirical Evidence. 6.5 Effects of Dependent Interviewing on Data Quality Across Surveys. 6.6 Open Issues. References. 7. Attitudes Over Time: The Psychology of Panel Conditioning (Patrick Sturgis, Nick Allum and Ian Brunton-Smith). 7.1 Introduction. 7.2 Panel Conditioning. 7.3 The Cognitive Stimulus Hypothesis. 7.4 Data and Measures. 7.5 Analysis. 7.6 Discussion. References. 8. Some Consequences of Survey Mode Changes in Longitudinal Surveys (Don A. Dillman). 8.1 Introduction. 8.2 Why Change Survey Modes in Longitudinal Surveys? 8.3 Why Changing Survey Mode Presents a Problem. 8.4 Conclusions. References. 9. Using Auxiliary Data for Adjustment in Longitudinal Research (Dirk Sikkel, Joop Hox and Edith de Leeuw). 9.1 Introduction. 9.2 Missing Data. 9.3 Calibration. 9.4 Calibrating Multiple Waves. 9.5 Differences Between Waves. 9.6 Single Imputation. 9.7 Multiple Imputation. 9.8 Conclusion and Discussion. References. 10. Identifying Factors Affecting Longitudinal Survey Response (Nicole Watson and Mark Wooden). 10.1 Introduction. 10.2 Factors Affecting Response and Attrition. 10.3 Predicting Response in the HILDA Survey. 10.4 Conclusion. References. 11. Keeping in Contact with Mobile Sample Members (Mick P. Couper and Mary Beth Ofstedal). 11.1 Introduction. 11.2 The Location Problem in Panel Surveys. 11.3 Case Study 1: Panel Study of Income Dynamics. 11.4 Case Study 2: Health and Retirement Study. 11.5 Discussion. References. 12. The Use of Respondent Incentives on Longitudinal Surveys (Heather Laurie and Peter Lynn). 12.1 Introduction. 12.2 Respondent Incentives on Cross-Sectional Surveys. 12.3 Respondent Incentives on Longitudinal Surveys. 12.4 Current Practice on Longitudinal Surveys. 12.5 Experimental Evidence on Longitudinal Surveys. 12.6 Conclusion. Acknowledgements. References. 13. Attrition in Consumer Panels (Robert D. Tortora). 13.1 Introduction. 13.2 The Gallup Poll Panel. 13.3 Attrition on the Gallup Poll Panel. 13.4 Summary. References. 14. Joint Treatment of Nonignorable Dropout and Informative Sampling. for Longitudinal Survey Data (Abdulhakeem A. H. Eideh and Gad Nathan). 14.1 Introduction. 14.2 Population Model. 14.3 Sampling Design and Sample Distribution. 14.4 Sample Distribution Under Informative Sampling and Informative Dropout. 14.5 Sample Likelihood and Estimation. 14.6 Empirical Example - British Labour Force Survey. 14.7 Conclusions. References. 15. Weighting and Calibration for Household Panels (Ulrich Rendtel and Torsten Harms). 15.1 Introduction. 15.2 Follow-up Rules. 15.3 Design-Based Estimation. 15.4 Calibration, 274. 15.5 Nonresponse and Attrition. 15.6 Summary. References. 16. Statistical Modelling for Structured Longitudinal Designs (Ian Plewis). 16.1 Introduction. 16.2 Methodological Framework. 16.3 The Data. 16.4 Modelling One Response from One Cohort. 16.5 Modelling One Response from More Than One Cohort. 16.6 Modelling More Than One Response from One Cohort. 16.7 Modelling Variation Between Generations. 16.8 Conclusion. References. 17. Using Longitudinal Surveys to Evaluate Interventions (Andrea Piesse, David Judkins and Graham Kalton). 17.1 Introduction. 17.2 Interventions, Outcomes and Longitudinal Data. 17.3 Youth Media Campaign Longitudinal Survey. 17.4 National Survey of Parents and Youth. 17.5 Gaining Early Awareness and Readiness for Undergraduate Programs (GEAR UP). 17.6 Concluding Remarks. References. 18. Robust Likelihood-Based Analysis of Longitudinal Survey Data with Missing Values (Roderick Little and Guangyu Zhang). 18.1 Introduction. 18.2 Multiple Imputation for Repeated-Measures Data. 18.3 Robust MAR Inference with a Single Missing Outcome. 18.4 Extensions of PSPP to Monotone and General Patterns. 18.5 Extensions to Inferences Other than Means. 18.6 Example. 18.7 Discussion. Acknowledgements. References. 19. Assessing the Temporal Association of Events Using Longitudinal Complex Survey Data (Norberto Pantoja-Galicia, Mary E. Thompson and Milorad). S. Kovacevic. 19.1 Introduction. 19.2 Temporal Order. 19.3 Nonparametric Density Estimation. 19.4 Survey Weights. 19.5 Application: The National Population Health Survey. 19.6 Application: The Survey of Labour and Income Dynamics. 19.7 Discussion. References. 20. Using Marginal Mean Models for Data from Longitudinal Surveys with a Complex Design: Some Advances in Methods (Georgia Roberts, Qunshu Ren and J.N.K. Rao). 20.1 Introduction. 20.2 Survey-Weighted GEE and Odds Ratio Approach. 20.3 Variance Estimation: One-Step EF-Bootstrap. 20.4 Goodness-of-Fit Tests. 20.5 Illustration Using NPHS Data. 20.6 Summary. References. 21. A Latent Class Approach for Estimating Gross Flows in the Presence of Correlated Classification Errors (Francesca Bassi and Ugo Trivellato). 21.1 Introduction. 21.2 Correlated Classification Errors and Latent Class Modelling. 21.3 The Data and Preliminary Evidence from Them. 21.4 A Model for Correlated Classification Errors in Retrospective Surveys. 21.5 Concluding Remarks. References. 22. A Comparison of Graphical Models and Structural Equation Models. for the Analysis of Longitudinal Survey Data )Peter W. F. Smith, Ann Berrington and Patrick Sturgis). 22.1 Introduction. 22.2 Conceptual Framework. 22.3 Graphical Chain Modelling Approach. 22.4 Structural Equation Modelling Approach. 22.5 Model Fitting. 22.6 Results. 22.7 Conclusions. References. Index.
£84.56
John Wiley & Sons Inc Bayesian Statistical Modelling
Book SynopsisBayesian methods combine the evidence from the data at hand with previous quantitative knowledge to analyse practical problems in a wide range of areas. The calculations were previously complex, but it is now possible to routinely apply Bayesian methods due to advances in computing technology and the use of new sampling methods for estimating parameters. Such developments together with the availability of freeware such as WINBUGS and R have facilitated a rapid growth in the use of Bayesian methods, allowing their application in many scientific disciplines, including applied statistics, public health research, medical science, the social sciences and economics. Following the success of the first edition, this reworked and updated book provides an accessible approach to Bayesian computing and analysis, with an emphasis on the principles of prior selection, identification and the interpretation of real data sets. The second edition: Provides an Trade Review"This text is ideal for researchers in applied statistics, medical sciences, public health and the social sciences, who will benefit greatly from the examples and applications featured. The book will also appeal to graduate students of applied statistics, data analysis and Bayesian methods, and will provide a great source of reference for both researchers and students." (Zentralblatt MATH, 2010) Table of ContentsPreface. Chapter 1 Introduction: The Bayesian Method, its Benefits and Implementation. Chapter 2 Bayesian Model Choice, Comparison and Checking. Chapter 3 The Major Densities and their Application. Chapter 4 Normal Linear Regression, General Linear Models and Log-Linear Models. Chapter 5 Hierarchical Priors for Pooling Strength and Overdispersed Regression Modelling. Chapter 6 Discrete Mixture Priors. Chapter 7 Multinomial and Ordinal Regression Models. Chapter 8 Time Series Models. Chapter 9 Modelling Spatial Dependencies. Chapter 10 Nonlinear and Nonparametric Regression. Chapter 11 Multilevel and Panel Data Models. Chapter 12 Latent Variable and Structural Equation Models for Multivariate Data. Chapter 13 Survival and Event History Analysis. Chapter 14 Missing Data Models. Chapter 15 Measurement Error, Seemingly Unrelated Regressions, and Simultaneous Equations. Appendix 1 A Brief Guide to Using WINBUGS. Index.
£82.60
John Wiley & Sons Inc Symbolic Data Analysis and the Sodas Software
Book SynopsisSymbolic data analysis is a relatively new field that provides a range of methods for analyzing complex datasets. Standard statistical methods do not have the power or flexibility to make sense of very large datasets, and symbolic data analysis techniques have been developed in order to extract knowledge from such data.Table of ContentsContributors. Foreword. Preface. ASSO Partners. Introduction. 1. The state of the art in symbolic data analysis: overview and future (Edwin Diday). PART I. DATABASES VERSUS SYMBOLIC OBJECTS. 2. Improved generation of symbolic objects from relational databases (Yves Lechevallier, Aicha El Golli and George Hébrail). 3. Exporting symbolic objects to databases (Donato Malerba, Floriana Esposito and Annalisa Appice). 4. A statistical metadata model for symbolic objects (Haralambos Papageorgiou and Maria Vardaki). 5. Editing symbolic data (Monique-Noirhomme-Fraiture, Paula Brito, Anne de Baenst-Vandenbroucke and Adolphe Nahimana). 6. The normal symbolic form (Marc Csernel and Francisco de A.T. de Carvalho). 7. Visualization (Monique-Noirhomme-Fraiture and Adolphe Nahimana). PART II. UNSUPERVISED METHODS. 8. Dissimilarity and matching (Floriana Esposito, Donato Malerba and Annalisa Appice). 9. Unsupervised divisive classification (Jean-Paul Rasson, Jean-Yves Pirçon, Pascale Lallemand and Séverine Adans). 10. Hierarchical and pyramidal clustering (Paula Brito and Francisco de A.T. de Carvalho). 11 .Clustering methods in symbolic data analysis (Francisco de A.T. de Carvalho, Yves Lechevallier and Rosanna Verde). 12. Visualizing symbolic data by Kohonen maps (Hans-Hermann Bock). 13 .Validation of clustering structure: determination of the number of clusters (André Hardy). 14. Stability measures for assessing a partition and its clusters: application to symbolic data sets (Patrice Bertrand and Ghazi Bel Mufti). 15. Principal component analysis of symbolic data described by intervals (N.Carlo Lauro, Rosanna Verde and Antonio Irpino). 16. Generalized canonical analysis (N.Carlo Lauro, Rosanna Verde and Antonio Irpino). PART III .SUPERVISED METHODS. 17. Bayesian decision trees (Jean-Paul Rasson, Pascale Lallemand and Séverine Adans). 18. Factor discriminant analysis (N.Carlo Lauro, Rosanna Verde and Antonio Irpino). 19. Symbolic linear regression methodology (Filipe Afonso, Lynne Billard, Edwin Diday and Mehdi Limam). 20. Multi-layer perceptrons and symbolic data (Fabrice Rossi and Brieuc Conan-Guez). PART IV. APPLICATION AND THE SODAS SOFTWARE. 21. Application to the Finnish, Spanish and Portuguese data of the European Social Survey (Soile Mustjärvi and Seppo Laaksonen). 22. People’s life values and trust components in Europe: symbolic data analysis for 20-22 countries (Seppo Laaksonen). 23. Symbolic analysis of the Time Use Survey in the Basque country (Marta Mas and Haritz Olaeta). 24. SODAS2 software: overview and methodology (Anne de Baenst-Vandenbroucke and Yves Lechevallier). Index.
£129.56
John Wiley & Sons Inc Quantitative Methods for Health Research
Book SynopsisQuantitative Research Methods for Health Professionals: A Practical Interactive Courseis a superb introduction to epidemiology, biostatistics, and research methodology for the whole health care community. Drawing examples from a wide range of health research, this practical handbook covers important contemporary health research methods such as survival analysis, Cox regression, and meta-analysis, the understanding of which go beyond introductory concepts. The book includes self-assessment exercises throughout to help students explore and reflect on their understanding and a clear distinction is made between a) knowledge and concepts that all students should ensure they understand and b) those that can be pursued by students who wish to do so. The authors incorporate a program of practical exercises in SPSS using a prepared data set that helps to consolidate the theory and develop skills and confidence in data handling, analysis and interpretation.Table of ContentsPreface. Acknowledgements. 1. Philosophy of science and introduction to epidemiology. Introduction and learning objectives. 1.1 Approaches to scientific research. 1.2 Formulating a research question. 1.3 Rates: incidence and prevalence. 1.4 Concepts of prevention. 1.5 Answers to self-assessment exercises. 2. Routine data sources and descriptive epidemiology. Introduction and learning objectives. 2.1 Routine collection of health information. 2.2 Descriptive epidemiology. 2.3 Information on the environment. 2.4 Displaying, describing and presenting data. 2.5 Summary of routinely available data. 2.6 Descriptive epidemiology in action. 2.7 Overview of epidemiological study designs. 2.8 Answers to self-assessment exercises. 3. Standardisation. Introduction and learning objectives. 3.1 Health inequalities in Merseyside. 3.2 Indirect standardisation: calculation of the standardised mortality ratio (SMR). 3.3 Direct standardisation. 3.4 Standardisation for factors other than age. 3.5 Answers to self-assessment exercises. 4. Surveys. Introduction and learning objectives. 4.1 Purpose and context. 4.2 Sampling methods. 4.3 The sampling frame. 4.4 Sampling error, confidence intervals and sample size . 4.5 Response. 4.6 Measurement. 4.7 Data types and presentation. 4.8 Answers to self-assessment exercises. 5. Cohort studies. Introduction and learning objectives. 5.1 Why do a cohort study?. 5.2 Obtaining the sample. 5.3 Measurement. 5.4 Follow-up. 5.5 Basic presentation and analysis of results. 5.6 How large should a cohort study be?. 5.7 Confounding. 5.8 Simple linear regression. 5.9 Introduction to multiple linear regression. 5.10 Answers to self-assessment exercises. 6. Case-control studies. Introduction and learning objectives. 6.1 Why do a case-control study?. 6.2 Key elements of study design. 6.3 Basic unmatched and matched analysis. 6.4 Sample size for a case-control study. 6.5 Confounding and logistic regression. 6.6 Answers to self-assessment exercises. 7. Intervention studies. Introduction and learning objectives. 7.1 Why do an intervention study?. 7.2 Key elements of intervention study design. 7.3 The analysis of intervention studies. 7.4 Testing more complex interventions. 7.5 How big should the trial be?. 7.6 Further aspects of intervention study design and analysis. 7.7 Answers to self-assessment exercises. 8. Life tables, survival analysis and Cox regression. Introduction and learning objectives. 8.1 Survival analysis. 8.2 Cox regression. 8.3 Current life tables. 8.4 Answers to self-assessment exercises. 9. Systematic reviews and meta analysis. Introduction and learning objectives. 9.1 The why and how of systematic reviews. 9.2 The methodology of meta-analysis. 9.3 Systematic reviews and meta-analyses of observational studies. 9.4 The Cochrane Collaboration. 9.5 Answers to self-assessment exercises. 10. Prevention strategies and evaluation of screening . Introduction and learning objectives. 10.1 Concepts of risk. 10.2 Strategies of prevention. 10.3 Evaluation of screening programmes. 10.4 Cohort and period effects. 10.5 Answers to self-assessment exercises. 11. Probability distributions, hypothesis testing and Bayesian methods. Introduction and learning objectives. 11.1 Probability distributions. 11.2 Data that do not ‘fit’ a probability distribution. 11.3 Hypothesis testing. 11.4 Choosing an appropriate hypothesis test. 11.5 Bayesian methods. 11.6 Answers to self-assessment exercises. Bibliography. Index.
£119.65
Wiley Statistical Matching
Book SynopsisThere is more statistical data produced in today's modern society than ever before. This data is analysed and cross-referenced for innumerable reasons. However, many data sets have no shared element and are harder to combine and therefore obtain any meaningful inference from.Trade Review"Those interested in statistical matching will find this book very useful." (Technometrics, August 2007) "My compliments to the authors for making these (seemingly) arcane ideas available to a whole new generation of statisticians and economists." (Journal of the American Statistical Association, September 2007)Table of ContentsPreface. 1 The Statistical Matching Problem. 1.1 Introduction. 1.2 The Statistical Framework. 1.3 The Missing Data Mechanism in the Statistical Matching Problem. 1.4 Accuracy of a Statistical Matching Procedure. 1.4.1 Model assumptions. 1.4.2 Accuracy of the estimator. 1.4.3 Representativeness of the synthetic file. 1.4.4 Accuracy of estimators applied on the synthetic data set. 1.5 Outline of the Book. 2 The Conditional Independence Assumption. 2.1 The Macro Approach in a Parametric Setting. 2.1.1 Univariate normal distributions case. 2.1.2 The multinormal case. 2.1.3 The multinomial case. 2.2 The Micro (Predictive) Approach in the Parametric Framework. 2.2.1 Conditional mean matching. 2.2.2 Draws based on conditional predictive distributions. 2.2.3 Representativeness of the predicted files. 2.3 Nonparametric Macro Methods. 2.4 The Nonparametric Micro Approach. 2.4.1 Random hot deck. 2.4.2 Rank hot deck. 2.4.3 Distance hot deck. 2.4.4 The matching noise. 2.5 Mixed Methods. 2.5.1 Continuous variables. 2.5.2 Categorical variables. 2.6 Comparison of Some Statistical Matching Procedures under the CIA. 2.7 The Bayesian Approach. 2.8 Other IdentifiableModels. 2.8.1 The pairwise independence assumption. 2.8.2 Finite mixture models. 3 Auxiliary Information. 3.1 Different Kinds of Auxiliary Information. 3.2 Parametric Macro Methods. 3.2.1 The use of a complete third file. 3.2.2 The use of an incomplete third file. 3.2.3 The use of information on inestimable parameters. 3.2.4 The multinormal case. 3.2.5 Comparison of different regression parameter estimators through simulation. 3.2.6 The multinomial case. 3.3 Parametric Predictive Approaches. 3.4 Nonparametric Macro Methods. 3.5 The Nonparametric Micro Approach with Auxiliary Information. 3.6 Mixed Methods. 3.6.1 Continuous variables. 3.6.2 Comparison between some mixed methods. 3.6.3 Categorical variables. 3.7 Categorical Constrained Techniques. 3.7.1 Auxiliary micro information and categorical constraints. 3.7.2 Auxiliary information in the form of categorical constraints. 3.8 The Bayesian Approach. 4 Uncertainty in Statistical Matching. 4.1 Introduction. 4.2 A Formal Definition of Uncertainty. 4.3 Measures of Uncertainty. 4.3.1 Uncertainty in the normal case. 4.3.2 Uncertainty in the multinomial case. 4.4 Estimation of Uncertainty. 4.4.1 Maximum likelihood estimation of uncertainty in the multinormal case. 4.4.2 Maximum likelihood estimation of uncertainty in the multinomial case. 4.5 Reduction of Uncertainty: Use of Parameter Constraints. 4.5.1 The multinomial case. 4.6 Further Aspects of Maximum Likelihood Estimation of Uncertainty. 4.7 An Example with Real Data. 4.8 Other Approaches to the Assessment of Uncertainty. 4.8.1 The consistent approach. 4.8.2 The multiple imputation approach. 4.8.3 The de Finetti coherence approach. 5 Statistical Matching and Finite Populations. 5.1 Matching Two Archives. 5.1.1 Definition of the CIA. 5.2 Statistical Matching and Sampling from a Finite Population. 5.3 Parametric Methods under the CIA. 5.3.1 The macro approach when the CIA holds. 5.3.2 The predictive approach. 5.4 Parametric Methods when Auxiliary Information is Available. 5.4.1 The macro approach. 5.4.2 The predictive approach. 5.5 File Concatenation. 5.6 Nonparametric Methods. 6 Issues in Preparing for Statistical Matching. 6.1 Reconciliation of Concepts and Definitions of Two Sources. 6.1.1 Reconciliation of biased sources. 6.1.2 Reconciliation of inconsistent definitions. 6.2 How to Choose the Matching Variables. 7 Applications. 7.1 Introduction. 7.2 Case Study: The Social Accounting Matrix. 7.2.1 Harmonization step. 7.2.2 Modelling the social accounting matrix. 7.2.3 Choosing the matching variables. 7.2.4 The SAM under the CIA. 7.2.5 The SAM and auxiliary information. 7.2.6 Assessment of uncertainty for the SAM. A Statistical Methods for Partially Observed Data. A.1 Maximum Likelihood Estimation with Missing Data. A.1.1 Missing data mechanisms. A.1.2 Maximum likelihood and ignorable nonresponse. A.2 Bayesian Inference withMissing Data. B Loglinear Models. B.1 Maximum Likelihood Estimation of the Parameters. C Distance Functions. D Finite Population Sampling. E R Code. E.1 The R Environment. E.2 R Code for Nonparametric Methods. E.3 R Code for Parametric and Mixed Methods. E.4 R Code for the Study of Uncertainty. E.5 Other R Functions. References. Index.
£81.86
John Wiley & Sons Inc Applied Mixed Models in Medicine 2e
Book SynopsisA mixed model allows the incorporation of both fixed and random variables within a statistical analysis. This enables efficient inferences and more information to be gained from the data. The application of mixed models is an increasingly popular way of analysing medical data, particularly in the pharmaceutical industry.Trade Review"…a valuable mixed model resource for most applied statisticians working in the medical environment." (Biometrics, June 2007) "…useful for practitioners and applied statisticians working in medical science." (Journal of the American Statistical Association, September 2007) "…takes a practical rather than theoretical approach and requires understanding of only basic statistics." (MAA Reviews, October 30, 2006) “This second edition gives an overview of the theory of mixed models and its application to real data in medical research.” (Zentralblatt MATH, April 2007)Table of ContentsPreface to Second Edition. Mixed Model Notations. 1 Introduction. 1.1 The Use of Mixed Models. 1.2 Introductory Example. 1.3 A Multi-Centre Hypertension Trial. 1.4 Repeated Measures Data. 1.5 More aboutMixed Models. 1.6 Some Useful Definitions. 2 NormalMixed Models. 2.1 Model Definition. 2.2 Model Fitting Methods. 2.3 The Bayesian Approach. 2.4 Practical Application and Interpretation. 2.5 Example. 3 Generalised Linear MixedModels. 3.1 Generalised Linear Models. 3.2 Generalised Linear Mixed Models. 3.3 Practical Application and Interpretation. 3.4 Example. 4 Mixed Models for Categorical Data. 4.1 Ordinal Logistic Regression (Fixed Effects Model). 4.2 Mixed Ordinal Logistic Regression. 4.3 Mixed Models for Unordered Categorical Data. 4.4 Practical Application and Interpretation. 4.5 Example. 5 Multi-Centre Trials and Meta-Analyses. 5.1 Introduction to Multi-Centre Trials. 5.2 The Implications of using Different Analysis Models. 5.3 Example: A Multi-Centre Trial. 5.4 Practical Application and Interpretation. 5.5 Sample Size Estimation. 5.6 Meta-Analysis. 5.7 Example: Meta-analysis. 6 RepeatedMeasures Data. 6.1 Introduction. 6.2 Covariance Pattern Models. 6.3 Example: Covariance Pattern Models for Normal Data. 6.4 Example: Covariance Pattern Models for Count Data. 6.5 Random Coefficients Models. 6.6 Examples of Random Coefficients Models. 6.7 Sample Size Estimation. 7 Cross-Over Trials. 7.1 Introduction. 7.2 Advantages of Mixed Models in Cross-Over Trials. 7.3 The AB/BA Cross-Over Trial. 7.4 Higher Order Complete Block Designs. 7.5 Incomplete Block Designs. 7.6 Optimal Designs. 7.7 Covariance Pattern Models. 7.8 Analysis of Binary Data. 7.9 Analysis of Categorical Data. 7.10 Use of Results from Random Effects Models in Trial Design. 7.11 General Points. 8 Other Applications of MixedModels. 8.1 Trials with Repeated Measurements within Visits. 8.2 Multi-Centre Trials with Repeated Measurements. 8.3 Multi-Centre Cross-Over Trials. 8.4 Hierarchical Multi-Centre Trials and Meta-Analysis. 8.5 Matched Case–Control Studies. 8.6 Different Variances for Treatment Groups in a Simple Between-Patient Trial. 8.7 Estimating Variance Components in an Animal Physiology Trial. 8.8 Inter- and Intra-Observer Variation in Foetal Scan Measurements. 8.9 Components of Variation and Mean Estimates in a Cardiology Experiment. 8.10 Cluster Sample Surveys. 8.11 Small AreaMortality Estimates. 8.12 Estimating Surgeon Performance. 8.13 Event History Analysis. 8.14 A Laboratory Study Using aWithin-Subject 4 × 4 Factorial Design. 8.15 Bioequivalence Studies with Replicate Cross-Over Designs. 8.16 Cluster Randomised Trials. 9 Software for Fitting MixedModels. 9.1 Packages for Fitting Mixed Models. 9.2 Basic use of PROC MIXED. 9.3 Using SAS to Fit Mixed Models to Non-Normal Data. Glossary. References. Index.
£95.36
John Wiley & Sons Inc Tutorials in Biostatistics Statistical Methods in
Book Synopsis"The Tutorials in Biostatistics" are a feature of the journal, "Statistics in Medicine" (SIM).Trade Review"The articles within the volume are self-contained, well written, and accessible to readers of widely ranging backgrounds. These volumes should be extremely valuable to practitioners…" (Journal of the American Statistical Association, December 2005) "The biostatistical practitioners who use a broad range of statistical methods would definitely find beneficial and useful to have 'Tutorials in Biostatistics'…" (E-STREAMS, September 2005) “ …this book gives a well-written and concise overview of selected biostatistical subjects.” (Journal of the Royal Statistical Society, Series A, June 2005)Table of ContentsPreface. Preface to Volume 1. Part I: OBSERVATIONAL STUDIES/EPIDEMIOLOGY. 1.1 Epidemiology. Computing Estimates of Incidence, including Lifetime Risk: Alzheimer’s Disease in the Framingham Study. The Practical Incidence Estimators (PIE) Macro. (Alexa Beiser et al). The Applications of Capture-Recapture Models to Epidemiological Data. (Anne Chao et al). 1.2 Adjustment Methods. Propensity Score Methods for Bias Reduction in the Comparison of a Treatment to a Non-Randomized Control Group (Ralph B. D’Agostino Jr.). 1.3 Agreement Statistics. Kappa Coefficients in Medical Research (Helen Chmura Kraemer et al). 1.4 Survival Models. Survival Analysis in Observational Studies (Kate Bull and David J. Spiegelhalter). Methods for Interval-Censored Data (Jane C. Lindsey and Louise M. Ryan). Analysis of Binary Outcomes in Longitudinal Studies Using Weighted Estimating Equations and Discrete-Time Survival Methods: Prevalence and Incidence of Smoking in an Adolescent Cohort (John B. Carlin et al). Part II: PROGNOSTIC/CLINICAL PREDICTION MODELS. 2.1 Prognostic Variables. Categorizing a Prognostic Variable: Review of Methods, Code for Easy Implementation and Applications to Decision-Making about Cancer Treatments (Madhu Mazumdar and Jill R. Glassman). 2.2 Prognostic/Clinical Prediction Models. Development of Health Risk Appraisal Functions in the Presence of Multiple Indicators: The Framingham Study Nursing Home Institutionalization Model (R. B. D’Agostino et al). Multivariable Prognostic Models: Issues in Developing Models, Evaluating Assumptions and Adequacy, and Measuring and Reducing Errors (Frank E. Harrell Jr et al). Development of a Clinical Prediction Model for an Ordinal Outcome: The World Health Organization Multicentre Study of Clinical Signs and Etiological Agents of Pneumonia, Sepsis and Meningitis in Young Infants (Frank E. Harrell Jr. et al). Using Observational Data to Estimate Prognosis: An Example Using a Coronary Artery Disease Registry (Elizabeth R. DeLong et al). Part III: CLINICAL TRIALS. 3.1 Design. Designing Studies for Dose Response (Weng Kee Wong and Peter A. Lachenbruch.). 3.2 Monitoring. Bayesian Data Monitoring in Clinical Trials (Peter M. Fayers et al). 3.3 Analysis. Longitudinal Data Analysis (Repeated Measures) in Clinical Trials (Paul S. Albert). Repeated Measures in Clinical Trials: Simple Strategies for Analysis Using Summary Measures (Stephen Senn et al). Strategies for Comparing Treatments on a Binary Response with Multi-Centre Data (Alan Agresti, and Jonathan Hartzel). A Review of Tests for Detecting a Monotone Dose–Response Relationship with Ordinal Response Data (Christy Chuang-Stein and Alan Agresti).
£180.86
Wiley Statistical Modelling of Complex Medical Data
a huge range and FREE tracked UK delivery on ALL orders.
£186.26
John Wiley & Sons Inc Structural Equation Modeling
Book SynopsisWinner of the 2008 Ziegel Prize for outstanding new book of the year Structural equation modeling (SEM) is a powerful multivariate method allowing the evaluation of a series of simultaneous hypotheses about the impacts of latent and manifest variables on other variables, taking measurement errors into account.Trade Review"This book is a welcome addition to any library and should be a valuable resource for research and teaching." (Technometrics, August 2008)Table of ContentsAbout the Author xi Preface xiii 1 Introduction 1 1.1 Standard Structural Equation Models 1 1.2 Covariance Structure Analysis 2 1.3 Why a New Book? 3 1.4 Objectives of the Book 4 1.5 Data Sets and Notations 6 Appendix 1.1 7 References 10 2 Some Basic Structural Equation Models 13 2.1 Introduction 13 2.2 Exploratory Factor Analysis 15 2.3 Confirmatory and Higher-order Factor Analysis Models 18 2.4 The LISREL Model 22 2.5 The Bentler–Weeks Model 26 2.6 Discussion 27 References 28 3 Covariance Structure Analysis 31 3.1 Introduction 31 3.2 Definitions, Notations and Preliminary Results 33 3.3 GLS Analysis of Covariance Structure 36 3.4 ml Analysis of Covariance Structure 41 3.5 Asymptotically Distribution-free Methods 44 3.6 Some Iterative Procedures 47 Appendix 3.1: Matrix Calculus 53 Appendix 3.2: Some Basic Results in Probability Theory 57 Appendix 3.3: Proofs of Some Results 59 References 65 4 Bayesian Estimation of Structural Equation Models 67 4.1 Introduction 67 4.2 Basic Principles and Concepts of Bayesian Analysis of SEMs 70 4.3 Bayesian Estimation of the CFA Model 81 4.4 Bayesian Estimation of Standard SEMs 95 4.5 Bayesian Estimation via WinBUGS 98 Appendix 4.1: The Metropolis–Hastings Algorithm 104 Appendix 4.2: EPSR Value 105 Appendix 4.3: Derivations of Conditional Distributions 106 References 108 5 Model Comparison and Model Checking 111 5.1 Introduction 111 5.2 Bayes Factor 113 5.3 Path Sampling 115 5.4 An Application: Bayesian Analysis of SEMs with Fixed Covariates 120 5.5 Other Methods 127 5.6 Discussion 130 Appendix 5.1: Another Proof of Equation (5.10) 131 Appendix 5.2: Conditional Distributions for Simulating (θ, ΩlY, t) 133 Appendix 5.3: PP p-values for Model Assessment 136 References 136 6 Structural Equation Models with Continuous and Ordered Categorical Variables 139 6.1 Introduction 139 6.2 The Basic Model 142 6.3 Bayesian Estimation and Goodness-of-fit 144 6.4 Bayesian Model Comparison 155 6.5 Application 1: Bayesian Selection of the Number of Factors in EFA 159 6.6 Application 2: Bayesian Analysis of Quality of Life Data 164 References 172 7 Structural Equation Models with Dichotomous Variables 175 7.1 Introduction 175 7.2 Bayesian Analysis 177 7.3 Analysis of a Multivariate Probit Confirmatory Factor Analysis Model 186 7.4 Discussion 190 Appendix 7.1: Questions Associated with the Manifest Variables 191 References 192 8 Nonlinear Structural Equation Models 195 8.1 Introduction 195 8.2 Bayesian Analysis of a Nonlinear SEM 197 8.3 Bayesian Estimation of Nonlinear SEMs with Mixed Continuous and Ordered Categorical Variables 215 8.4 Bayesian Estimation of SEMs with Nonlinear Covariates and Latent Variables 220 8.5 Bayesian Model Comparison 230 References 239 9 Two-level Nonlinear Structural Equation Models 243 9.1 Introduction 243 9.2 A Two-level Nonlinear SEM with Mixed Type Variables 244 9.3 Bayesian Estimation 247 9.4 Goodness-of-fit and Model Comparison 255 9.5 An Application: Filipina CSWs Study 259 9.6 Two-level Nonlinear SEMs with Cross-level Effects 267 9.7 Analysis of Two-level Nonlinear SEMs using WinBUGS 275 Appendix 9.1: Conditional Distributions: Two-level Nonlinear Sem 279 Appendix 9.2: MH Algorithm: Two-level Nonlinear SEM 283 Appendix 9.3: PP p-value for Two-level NSEM with Mixed Continuous and Ordered-categorical Variables 285 Appendix 9.4: Questions Associated with the Manifest Variables 286 Appendix 9.5: Conditional Distributions: SEMs with Cross-level Effects 286 Appendix 9.6: The MH algorithm: SEMs with Cross-level Effects 289 References 290 10 Multisample Analysis of Structural Equation Models 293 10.1 Introduction 293 10.2 The Multisample Nonlinear Structural Equation Model 294 10.3 Bayesian Analysis of Multisample Nonlinear SEMs 297 10.4 Numerical Illustrations 302 Appendix 10.1: Conditional Distributions: Multisample SEMs 313 References 316 11 Finite Mixtures in Structural Equation Models 319 11.1 Introduction 319 11.2 Finite Mixtures in SEMs 321 11.3 Bayesian Estimation and Classification 323 11.4 Examples and Simulation Study 330 11.5 Bayesian Model Comparison of Mixture SEMs 344 Appendix 11.1: The Permutation Sampler 351 Appendix 11.2: Searching for Identifiability Constraints 352 References 352 12 Structural Equation Models with Missing Data 355 12.1 Introduction 355 12.2 A General Framework for SEMs with Missing Data that are Mar 357 12.3 Nonlinear SEM with Missing Continuous and Ordered Categorical Data 359 12.4 Mixture of SEMs with Missing Data 370 12.5 Nonlinear SEMs with Nonignorable Missing Data 375 12.6 Analysis of SEMs with Missing Data via WinBUGS 386 Appendix 12.1: Implementation of the MH Algorithm 389 References 390 13 Structural Equation Models with Exponential Family of Distributions 393 13.1 Introduction 393 13.2 The SEM Framework with Exponential Family of Distributions 394 13.3 A Bayesian Approach 398 13.4 A Simulation Study 402 13.5 A Real Example: A Compliance Study of Patients 404 13.6 Bayesian Analysis of an Artificial Example using WinBUGS 411 13.7 Discussion 416 Appendix 13.1: Implementation of the MH Algorithms 417 Appendix 13.2 419 References 419 14 Conclusion 421 References 425 Index 427
£92.66
John Wiley & Sons Inc Basic Biostatistics for Geneticists and
Book SynopsisAnyone who attempts to read genetics or epidemiology research literature needs to understand the essentials of biostatistics. This book, a revised new edition of the successful Essentials of Biostatistics has been written to provide such an understanding to those who have little or no statistical background and who need to keep abreast of new findings in this fast moving field. Unlike many other elementary books on biostatistics, the main focus of this book is to explain basic concepts needed to understand statistical procedures. This Book: Surveys basic statistical methods used in the genetics and epidemiology literature, including maximum likelihood and least squares. Introduces methods, such as permutation testing and bootstrapping, that are becoming more widely used in both genetic and epidemiological research. Is illustrated throughout with simple examples to clarify the statistical methodology. Explains Bayes' theorem pictoTrade Review"The book is unusual in having less ambitious goals than the average statistics textbook. The focus is not to teach applications but, as the preface maintains, simply to enable readers to knowledgeably read the new literature, to understand the statistical methods used, and thereby to better keep abreast of new findings in epidemiology and genetics." (JAMA, September 13, 2010) "This is a well-written and comprehensive review of the basic (and not-so-basic) concepts and techniques in biostatistics. It is understandable to biologists and clinicians, while still providing useful pointers and reminders to statisticians. It is worth a place on the bookshelves of all researchers in genetics, regardless of their statistical expertise." (Human Genetics, February 2010) "Anyone who wishes to critically read biomedical literature will find the knowledge gained from reading [the text] of great value." (American Journal of Epidemiology, 2009) Table of ContentsPreface ix 1 Introduction: The Role and Relevance of Statistics, Genetics and Epidemiology In Medicine 3 Why Biostatistics? 3 What Exactly is (are) Statistics? 5 Reasons for Understanding Statistics 6 What Exactly is Genetics? 8 What Exactly is Epidemiology? 10 How Can a Statistician Help Geneticists and Epidemiologists? 11 Disease Prevention versus Disease Therapy 12 A Few Examples: Genetics, Epidemiology and Statistical Inference 12 Summary 14 References 15 2 Populations, Samples, and Study Design 19 The Study of Cause and Effect 19 Populations, Target Populations and Study Units 21 Probability Samples and Randomization 23 Observational Studies 25 Family Studies 27 Experimental Studies 28 Quasi-Experimental Studies 36 Summary 37 Further Reading 38 Problems 38 3 Descriptive Statistics 45 Why Do We Need Descriptive Statistics? 45 Scales of Measurement 46 Tables 47 Graphs 49 Proportions and Rates 55 Relative Measures of Disease Frequency 58 Sensitivity, Specificity and Predictive Values 61 Measures of Central Tendency 62 Measures of Spread or Variability 64 Measures of Shape 67 Summary 68 Further Reading 70 Problems 70 4 The Laws of Probability 79 Definition of Probability 79 The Probability of Either of Two Events: A or B 82 The Joint Probability of Two Events: A and B 83 Examples of Independence, Nonindependence and Genetic Counseling 86 Bayes’ Theorem 89 Likelihood Ratio 97 Summary 98 Further Reading 99 Problems 99 5 Random Variables and Distributions 107 Variability and Random Variables 107 Binomial Distribution 109 A Note about Symbols 112 Poisson Distribution 113 Uniform Distribution 114 Normal Distribution 116 Cumulative Distribution Functions 119 The Standard Normal (Gaussian) Distribution 120 Summary 122 Further Reading 123 Problems 123 6 Estimates and Confidence Limits 131 Estimates and Estimators 131 Notation for Population Parameters, Sample Estimates, and Sample Estimators 133 Properties of Estimators 134 Maximum Likelihood 135 Estimating Intervals 137 Distribution of the Sample Mean 138 Confidence Limits 140 Summary 146 Problems 148 7 Significance Tests and Tests of Hypotheses 155 Principle of Significance Testing 155 Principle of Hypothesis Testing 156 Testing a Population Mean 157 One-Sided versus Two-Sided Tests 160 Testing a Proportion 161 Testing the Equality of Two Variances 165 Testing the Equality of Two Means 167 Testing the Equality of Two Medians 169 Validity and Power 172 Summary 176 Further Reading 178 Problems 178 8 Likelihood Ratios, Bayesian Methods and Multiple Hypotheses 187 Likelihood Ratios 187 Bayesian Methods 190 Bayes’ Factors 192 Bayesian Estimates and Credible Intervals 194 The Multiple Testing Problem 195 Summary 198 Problems 199 9 The Many Uses of Chi-Square 203 The Chi-Square Distribution 203 Goodness-of-Fit Tests 206 Contingency Tables 209 Inference About the Variance 219 Combining p-Values 220 Likelihood Ratio Tests 221 Summary 223 Further Reading 225 Problems 225 10 Correlation and Regression 233 Simple Linear Regression 233 The Straight-Line Relationship When There is Inherent Variability 240 Correlation 242 Spearman’s Rank Correlation 246 Multiple Regression 246 Multiple Correlation and Partial Correlation 250 Regression toward the Mean 251 Summary 253 Further Reading 254 Problems 255 11 Analysis of Variance and Linear Models 265 Multiple Treatment Groups 265 Completely Randomized Design with a Single Classification of Treatment Groups 267 Data with Multiple Classifications 269 Analysis of Covariance 281 Assumptions Associated with the Analysis of Variance 282 Summary 283 Further Reading 284 Problems 285 12 Some Specialized Techniques 293 Multivariate Analysis 293 Discriminant Analysis 295 Logistic Regression 296 Analysis of Survival Times 299 Estimating Survival Curves 301 Permutation Tests 304 Resampling Methods 309 Summary 312 Further Reading 313 Problems 313 13 Guides to a Critical Evaluation of Published Reports 321 The Research Hypothesis 321 Variables Studied 321 The Study Design 322 Sample Size 322 Completeness of the Data 323 Appropriate Descriptive Statistics 323 Appropriate Statistical Methods for Inferences 323 Logic of the Conclusions 324 Meta-analysis 324 Summary 326 Further Reading 327 Problems 328 Epilogue 329 Review Problems 331 Answers to Odd-Numbered Problems 345 Appendix 353 Index 365
£97.16
John Wiley & Sons Inc Basic Biostatistics for Geneticists and
Book SynopsisAnyone who attempts to read genetics or epidemiology research literature needs to understand the essentials of biostatistics. This book, a revised new edition of the successful Essentials of Biostatistics has been written to provide such an understanding to those who have little or no statistical background and who need to keep abreast of new findings in this fast moving field. Unlike many other elementary books on biostatistics, the main focus of this book is to explain basic concepts needed to understand statistical procedures. This Book: Surveys basic statistical methods used in the genetics and epidemiology literature, including maximum likelihood and least squares. Introduces methods, such as permutation testing and bootstrapping, that are becoming more widely used in both genetic and epidemiological research. Is illustrated throughout with simple examples to clarify the statistical methodology. Explains Bayes' theorem pictoTrade Review"The book is unusual in having less ambitious goals than the average statistics textbook. The focus is not to teach applications but, as the preface maintains, simply to enable readers to knowledgeably read the new literature, to understand the statistical methods used, and thereby to better keep abreast of new findings in epidemiology and genetics." (JAMA, September 13, 2010) "This is a well-written and comprehensive review of the basic (and not-so-basic) concepts and techniques in biostatistics. It is understandable to biologists and clinicians, while still providing useful pointers and reminders to statisticians. It is worth a place on the bookshelves of all researchers in genetics, regardless of their statistical expertise." (Human Genetics, February 2010) "Anyone who wishes to critically read biomedical literature will find the knowledge gained from reading [the text] of great value." (American Journal of Epidemiology, 2009) Table of ContentsPreface ix 1 Introduction: The Role and Relevance of Statistics, Genetics and Epidemiology In Medicine 3 Why Biostatistics? 3 What Exactly is (Are) Statistics? 5 Reasons for Understanding Statistics 6 What Exactly is Genetics? 8 What Exactly is Epidemiology? 10 How Can a Statistician Help Geneticists and Epidemiologists? 11 Disease Prevention versus Disease Therapy 12 A Few Examples: Genetics, Epidemiology and Statistical Inference 12 Summary 14 References 15 2 Populations, Samples, and Study Design 19 The Study of Cause and Effect 19 Populations, Target Populations and Study Units 21 Probability Samples and Randomization 23 Observational Studies 25 Family Studies 27 Experimental Studies 28 Quasi-Experimental Studies 36 Summary 37 Further Reading 38 Problems 38 3 Descriptive Statistics 45 Why Do We Need Descriptive Statistics? 45 Scales of Measurement 46 Tables 47 Graphs 49 Proportions and Rates 55 Relative Measures of Disease Frequency 58 Sensitivity, Specificity and Predictive Values 61 Measures of Central Tendency 62 Measures of Spread or Variability 64 Measures of Shape 67 Summary 68 Further Reading 70 Problems 70 4 The Laws of Probability 79 Definition of Probability 79 The Probability of Either of Two Events: A or B 82 The Joint Probability of Two Events: A and B 83 Examples of Independence, Nonindependence and Genetic Counseling 86 Bayes’ Theorem 89 Likelihood Ratio 97 Summary 98 Further Reading 99 Problems 99 5 Random Variables and Distributions 107 Variability and Random Variables 107 Binomial Distribution 109 A Note about Symbols 112 Poisson Distribution 113 Uniform Distribution 114 Normal Distribution 116 Cumulative Distribution Functions 119 The Standard Normal (Gaussian) Distribution 120 Summary 122 Further Reading 123 Problems 123 6 Estimates and Confidence Limits 131 Estimates and Estimators 131 Notation for Population Parameters, Sample Estimates, and Sample Estimators 133 Properties of Estimators 134 Maximum Likelihood 135 Estimating Intervals 137 Distribution of the Sample Mean 138 Confidence Limits 140 Summary 146 Problems 148 7 Significance Tests and Tests of Hypotheses 155 Principle of Significance Testing 155 Principle of Hypothesis Testing 156 Testing a Population Mean 157 One-Sided versus Two-Sided Tests 160 Testing a Proportion 161 Testing the Equality of Two Variances 165 Testing the Equality of Two Means 167 Testing the Equality of Two Medians 169 Validity and Power 172 Summary 176 Further Reading 178 Problems 178 8 Likelihood Ratios, Bayesian Methods and Multiple Hypotheses 187 Likelihood Ratios 187 Bayesian Methods 190 Bayes’ Factors 192 Bayesian Estimates and Credible Intervals 194 The Multiple Testing Problem 195 Summary 198 Problems 199 9 The Many Uses of Chi-Square 203 The Chi-Square Distribution 203 Goodness-of-Fit Tests 206 Contingency Tables 209 Inference About the Variance 219 Combining p-Values 220 Likelihood Ratio Tests 221 Summary 223 Further Reading 225 Problems 225 10 Correlation and Regression 233 Simple Linear Regression 233 The Straight-Line Relationship When There is Inherent Variability 240 Correlation 242 Spearman’s Rank Correlation 246 Multiple Regression 246 Multiple Correlation and Partial Correlation 250 Regression toward the Mean 251 Summary 253 Further Reading 254 Problems 255 11 Analysis of Variance and Linear Models 265 Multiple Treatment Groups 265 Completely Randomized Design with a Single Classification of Treatment Groups 267 Data with Multiple Classifications 269 Analysis of Covariance 281 Assumptions Associated with the Analysis of Variance 282 Summary 283 Further Reading 284 Problems 285 12 Some Specialized Techniques 293 Multivariate Analysis 293 Discriminant Analysis 295 Logistic Regression 296 Analysis of Survival Times 299 Estimating Survival Curves 301 Permutation Tests 304 Resampling Methods 309 Summary 312 Further Reading 313 Problems 313 13 Guides To a Critical Evaluation of Published Reports 321 The Research Hypothesis 321 Variables Studied 321 The Study Design 322 Sample Size 322 Completeness of the Data 323 Appropriate Descriptive Statistics 323 Appropriate Statistical Methods for Inferences 323 Logic of the Conclusions 324 Meta-analysis 324 Summary 326 Further Reading 327 Problems 328 Epilogue 329 Review Problems 331 Answers to Odd-Numbered Problems 345 Appendix 353 Index 365
£38.90
John Wiley & Sons Inc Fundamental Probability A Computational Approach
Book SynopsisThis publication provides an introduction to the theory and techniques of probability and grew from a set of notes written by the author to accompany a two semester course consisting of senior undergraduate and first year graduate students from quantitative business (50%), economics (40%) and mathematics (10% ).Trade Review"The collection is sure to be a set of remarkable references for students and teachers alike." (The American Statistician, May 2008) "Very enjoyable and instructive reading." (CHOICE, November 2006) "...a very good book which might, I hope, be standard for introductory courses in probability theory during next years." (Zentralbatt MATH, 11th March 2007)Table of ContentsPreface. A note to the student (and instructor). A note to the instructor (and student). Acknowledgements. Introduction. PART I: BASIC PROBABILITY. 1. Combinatorics. 1.1 Basic counting. 1.2 Generalized binomial coefficients. 1.3 Combinatoric identities and the use of induction. 1.4 The binomial and multinomial theorems. 1.4.1 The binomial theorem. 1.4.2 An extension of the binomial theorem. 1.4.3 The multinomial theorem. 1.5 The gamma and beta functions. 1.5.1 The gamma function. 1.5.2 The beta function. 1.6 Problems. 2. Probability spaces and counting. 2.1 Introducing counting and occupancy problems. 2.2 Probability spaces. 2.2.1 Introduction. 2.2.2 Definitions. 2.3 Properties. 2.3.1 Basic properties. 2.3.2 Advanced properties. 2.3.3 A theoretical property. 2.4 Problems. 3. Symmetric spaces and conditioning. 3.1 Applications with symmetric probability spaces. 3.2 Conditional probability and independence. 3.2.1 Total probability and Bayes’ rule. 3.2.2 Extending the law of total probability. 3.2.3 Statistical paradoxes and fallacies. 3.3 The problem of the points. 3.3.1 Three solutions. 3.3.2 Further gambling problems. 3.3.3 Some historical references. 3.4 Problems. PART II: DISCRETE RANDOM VARIABLES. 4. Univariate random variables. 4.1 Definitions and properties. 4.1.1 Basic definitions and properties. 4.1.2 Further definitions and properties. 4.2 Discrete sampling schemes. 4.2.1 Bernoulli and binomial. 4.2.2 Hypergeometric. 4.2.3 Geometric and negative binomial. 4.2.4 Inverse hypergeometric. 4.2.5 Poisson approximations. 4.2.6 Occupancy distributions. 4.3 Transformations. 4.4 Moments. 4.4.1 Expected value of X. 4.4.2 Higher-order moments. 4.4.3 Jensen?s inequality. 4.5 Poisson processes. 4.6 Problems. 5. Multivariate random variables. 5.1 Multivariate density and distribution. 5.1.1 Joint cumulative distribution functions. 5.1.2 Joint probability mass and density functions. 5.2 Fundamental properties of multivariate random variables. 5.2.1 Marginal distributions. 5.2.2 Independence. 5.2.3 Exchangeability. 5.2.4 Transformations. 5.2.5 Moments. 5.3 Discrete sampling schemes. 5.3.1 Multinomial. 5.3.2 Multivariate hypergeometric. 5.3.3 Multivariate negative binomial. 5.3.4 Multivariate inverse hypergeometric. 5.4 Problems. 6. Sums of random variables. 6.1 Mean and variance. 6.2 Use of exchangeable Bernoulli random variables. 6.2.1 Examples with birthdays. 6.3 Runs distributions. 6.4 Random variable decomposition. 6.4.1 Binomial, negative binomial and Poisson. 6.4.2 Hypergeometric. 6.4.3 Inverse hypergeometric. 6.5 General linear combination of two random variables. 6.6 Problems. PART III: CONTINUOUS RANDOM VARIABLES. 7. Continuous univariate random variables. 7.1 Most prominent distributions. 7.2 Other popular distributions. 7.3 Univariate transformations. 7.3.1 Examples of one-to-one transformations. 7.3.2 Many-to-one transformations. 7.4 The probability integral transform. 7.4.1 Simulation. 7.4.2 Kernel density estimation. 7.5 Problems. 8. Joint and conditional random variables. 8.1 Review of basic concepts. 8.2 Conditional distributions. 8.2.1 Discrete case. 8.2.2 Continuous case. 8.2.3 Conditional moments. 8.2.4 Expected shortfall. 8.2.5 Independence. 8.2.6 Computing probabilities via conditioning. 8.3 Problems. 9. Multivariate transformations. 9.1 Basic transformation. 9.2 The t and F distributions. 9.3 Further aspects and important transformations. 9.4 Problems. Appendix A. Calculus review. Appendix B. Notation tables. Appendix C. Distribution tables. References. Index.
£97.16
John Wiley & Sons Inc Intermediate Probability
Book SynopsisIntermediate Probability is the natural extension of the author''s Fundamental Probability. It details several highly important topics, from standard ones such as order statistics, multivariate normal, and convergence concepts, to more advanced ones which are usually not addressed at this mathematical level, or have never previously appeared in textbook form. The author adopts a computational approach throughout, allowing the reader to directly implement the methods, thus greatly enhancing the learning experience and clearly illustrating the applicability, strengths, and weaknesses of the theory. The book: Places great emphasis on the numeric computation of convolutions of random variables, via numeric integration, inversion theorems, fast Fourier transforms, saddlepoint approximations, and simulation. Provides introductory material to required mathematical topics such as complex numbers, Laplace and Fourier transforms, matrix algebra, confluent hypergeometricTrade Review"I thoroughly enjoyed Intermediate Probability. I was so thrilled with it that I have shared it with some of my colleagues. They have called it a 'gold mine' of problems and resources, and describing it as 'amazing.' ... I highly recommend it." (Journal of the American Statistical Association, September 2009) "The reader-friendly style of the text itself would make the book appropriate for self-study or classroom adoption." (MAA Reviews, December 2007) Table of ContentsPreface. I Sums of Random Variables. 1 Generating functions. 1.1 The moment generating function. 1.2 Characteristic functions. 1.3 Use of the fast Fourier transform. 1.4 Multivariate case. 1.5 Problems. 2 Sums and other functions of several random variables. 2.1 Weighted sums of independent random variables. 2.2 Exact integral expressions for functions of two continuous random variables. 2.3 Approximating the mean and variance. 2.4 Problems. 3 The multivariate normal distribution. 3.1 Vector expectation and variance. 3.2 Basic properties of the multivariate normal. 3.3 Density and moment generating function. 3.4 Simulation and c.d.f. calculation. 3.5 Marginal and conditional normal distributions. 3.6 Partial correlation. 3.7 Joint distribution of Xbar and S2 for i.i.d. normal samples. 3.8 Matrix algebra. 3.9 Problems. II Asymptotics and Other Approximations. 4 Convergence concepts. 4.1 Inequalities for random variables. 4.2 Convergence of sequences of sets. 4.3 Convergence of sequences of random variables. 4.4 The central limit theorem. 4.5 Problems. 5 Saddlepoint approximations. 5.1 Univariate. 5.2 Multivariate. 5.3 The hypergeometric functions 1F1 and 2F1. 5.4 Problems. 6 Order statistics. 6.1 Distribution theory for i.i.d. samples. 6.2 Further examples. 6.3 Distribution theory for dependent samples. 6.4 Problems. III More Flexible and Advanced Random Variables. 7 Generalizing and mixing. 7.1 Basic methods of extension. 7.2 Weighted sums of independent random variables. 7.3 Mixtures. 7.4 Problems. 8 The stable Paretian distribution. 8.1 Symmetric stable. 8.2 Asymmetric stable. 8.3 Moments. 8.4 Simulation. 8.5 Generalized central limit theorem. 9 Generalized inverse Gaussian and generalized hyperbolic distributions. 9.1 Introduction. 9.2 The modified Bessel function of the third kind. 9.3 Mixtures of normal distributions. 9.4 The generalized inverse Gaussian distribution. 9.5 The generalized hyperbolic distribution. 9.6 Properties of the GHyp distribution family. 9.7 Problems. 10 Noncentral distributions. 10.1 Noncentral chi-square. 10.2 Singly and doubly noncentral F. 10.3 Noncentral beta. 10.4 Singly and doubly noncentral t. 10.5 Saddlepoint uniqueness for the doubly noncentral F. 10.6 Problems. A Notation and distribution tables. References. Index.
£114.26
Wiley RegisterBased Statistics
Book SynopsisThere is a growing interest in developing register-based surveys; that is surveys based upon already available administrative data. Since huge amounts of such data are generated within various administrative systems, the opportunity exists to use the data for statistical analysis without any of the costs involved in data collection. Register-based surveys require their own methodology and the development of these methods is an important challenge to statistical science. Instead of methods on how to collect data, methods for integrating data from different sources are necessary. How should administrative data be transformed to meet the statistical needs? Register-based Statistics offers readers a detailed account of the principles and practices of this increasingly popular area of statistics. Provides a comprehensive overview of register-based statistics, both in terms of theory and advanced application. Uses real life examples taken from StatistiTrade Review"I believe that sufficient practical information is provided to make the book worth reading." (Technometrics, November 2008) "I believe that sufficient practical information is provided to make the book worth reading." (Technometrics, Nov 2008) Table of ContentsPreface. Chapter 1. Register-based surveys – an introduction. 1.1 Do we need a theory on register-based surveys? 1.2 What is a statistical survey? 1.3 What is a register? 1.4 What is a register-based survey? 1.5 Administrative and statistical information systems. 1.6 Why should statistics be based on administrative data? 1.7 An overview of this book. Chapter 2. How to structure a register system. 2.1 Object types and relations. 2.2 The system of base registers. 2.3 Standardised variables in the register system. 2.4 The register system as a whole. 2.5 Building and using the system. 2.6 Statistical register systems outside Statistics Sweden. Chapter 3. A terminology for register-based surveys. 3.1 Terminology – different language. 3.2 Register terms. 3.3 Terms for different kinds of variables. Chapter 4. Sample surveys and registers. 4.1 How can sample surveys benefit by the register system? 4.2 How can register-based surveys and sample surveys be combined? 4.3 Comparing sample surveys and register-based surveys. Chapter 5. How to create a register – the population. 5.1 How should register-based surveys be structured? 5.2 Determining the research objectives. 5.3 The inventory phase – making an inventory of different sources. 5.4 Defining a register’s object set. 5.5 Defining and deriving objects. 5.6 How to produce regional register-based statistics. Chapter 6. How to create a register – the variables. 6.1 Deciding the register's variable content. 6.2 Forming derived variables using models. 6.3 Editing and correcting register variables. 6.4 Creating longitudinal registers. Chapter 7. Estimation methods. 7.1 Estimation in sample surveys and register-based surveys. 7.2 Fundamental estimation methods in register-based surveys. 7.3 Using weights in register-based surveys. 7.4 Estimation methods using weights – calendar year registers. 7.5 Calibration of weights in register-based surveys. Chapter 8. Calibration and imputation. 8.1 The nonresponse problem. 8.2 Estimation methods to correct for overcoverage. 8.3 Estimation methods to correct for level shifts in time series. Chapter 9. Estimation with combination objects. 9.1 Aggregation errors. 9.2 Estimation methods for multi-valued variables. 9.3 Linking of time series at micro level using combination objects. Chapter 10. Quality of register-based statistics. 10.1 Specific quality issues for register-based statistics? 10.2 Comparing errors in sample surveys and register-based surveys. 10.3 The users’ and the producers’ view of quality. 10.4 Detailed knowledge of the characteristics of a register. 10.3 Overall appraisal of quality. Chapter 11. Metadata and IT-systems. 11.1 Primary registers – the need for metadata. 11.2 Changes over time – the need for metadata. 11.3 Integrated registers – the need for metadata. 11.4 Classification and definitions database. 11.5 The need for metadata for registers. 11.6 IT systems for register-based statistics. Chapter 12. Protection of privacy and confidentiality. 12.1 Internal security. 12.2 Disclosure risks – tables. 12.3 Disclosure risks – micro data. Chapter 13. Coordination and coherence. 13.1 Content-related coordination. 13.2 Coherence. 13.3 Consistent and coherent enterprise statistics. Chapter 14. Conclusions. References. Glossary. Index.
£95.36
John Wiley & Sons Inc Statistical Monitoring of Complex Multivatiate
Book SynopsisStatistical Monitoring of Complex Multivariate Processes summarizes recent advances in statistical-based process monitoring of complex multivariate process systems. The book includes a broad range of applications of multivariate statistical techniques into the area of mechanical, manufacturing, and power engineering.Table of ContentsPreface xiii Acknowledgements xvii Abbreviations xix Symbols xxi Nomenclature xxiii Introduction xxv Part I Fundamentals of Multivariate Statistical Process Control 1 1 Motivation for multivariate statistical process control 3 1.1 Summary of statistical process control 3 1.1.1 Roots and evolution of statistical process control 4 1.1.2 Principles of statistical process control 5 1.1.3 Hypothesis testing, Type I and II errors 12 1.2 Why multivariate statistical process control 15 1.2.1 Statistically uncorrelated variables 16 1.2.2 Perfectly correlated variables 17 1.2.3 Highly correlated variables 19 1.2.4 Type I and II errors and dimension reduction 24 1.3 Tutorial session 26 2 Multivariate data modeling methods 28 2.1 Principal component analysis 30 2.1.1 Assumptions for underlying data structure 30 2.1.2 Geometric analysis of data structure 33 2.1.3 A simulation example 34 2.2 Partial least squares 38 2.2.1 Assumptions for underlying data structure 39 2.2.2 Deflation procedure for estimating data models 41 2.2.3 A simulation example 43 2.3 Maximum redundancy partial least squares 49 2.3.1 Assumptions for underlying data structure 49 2.3.2 Source signal estimation 50 2.3.3 Geometric analysis of data structure 52 2.3.4 A simulation example 58 2.4 Estimating the number of source signals 65 2.4.1 Stopping rules for PCA models 65 2.4.2 Stopping rules for PLS models 76 2.5 Tutorial Session 79 3 Process monitoring charts 81 3.1 Fault detection 83 3.1.1 Scatter diagrams 84 3.1.2 Non-negative quadratic monitoring statistics 85 3.2 Fault isolation and identification 93 3.2.1 Contribution charts 95 3.2.2 Residual-based tests 98 3.2.3 Variable reconstruction 100 3.3 Geometry of variable projections 111 3.3.1 Linear dependency of projection residuals 111 3.3.2 Geometric analysis of variable reconstruction 112 3.4 Tutorial session 119 Part II Application Studies 121 4 Application to a chemical reaction process 123 4.1 Process description 123 4.2 Identification of a monitoring model 124 4.3 Diagnosis of a fault condition 133 5 Application to a distillation process 141 5.1 Process description 141 5.2 Identification of a monitoring model 144 5.3 Diagnosis of a fault condition 153 Part III Advances in Multivariate Statistical Process Control 165 6 Further modeling issues 167 6.1 Accuracy of estimating PCA models 168 6.1.1 Revisiting the eigendecomposition of Sz0z0 168 6.1.2 Two illustrative examples 171 6.1.3 Maximum likelihood PCA for known Sgg 172 6.1.4 Maximum likelihood PCA for unknown Sgg 177 6.1.5 A simulation example 182 6.1.6 A stopping rule for maximum likelihood PCA models 187 6.1.7 Properties of model and residual subspace estimates 189 6.1.8 Application to a chemical reaction process – revisited 194 6.2 Accuracy of estimating PLS models 202 6.2.1 Bias and variance of parameter estimation 203 6.2.2 Comparing accuracy of PLS and OLS regression models 205 6.2.3 Impact of error-in-variables structure upon PLS models 212 6.2.4 Error-in-variable estimate for known See 218 6.2.5 Error-in-variable estimate for unknown See 219 6.2.6 Application to a distillation process – revisited 223 6.3 Robust model estimation 226 6.3.1 Robust parameter estimation 228 6.3.2 Trimming approaches 231 6.4 Small sample sets 232 6.5 Tutorial session 237 7 Monitoring multivariate time-varying processes 240 7.1 Problem analysis 241 7.2 Recursive principal component analysis 242 7.3 Moving window principal component analysis 244 7.3.1 Adapting the data correlation matrix 244 7.3.2 Adapting the eigendecomposition 247 7.3.3 Computational analysis of the adaptation procedure 251 7.3.4 Adaptation of control limits 252 7.3.5 Process monitoring using an application delay 253 7.3.6 Minimum window length 254 7.4 A simulation example 257 7.4.1 Data generation 257 7.4.2 Application of PCA 258 7.4.3 Utilizing MWPCA based on an application delay 261 7.5 Application to a Fluid Catalytic Cracking Unit 265 7.5.1 Process description 266 7.5.2 Data generation 268 7.5.3 Pre-analysis of simulated data 272 7.5.4 Application of PCA 273 7.5.5 Application of MWPCA 275 7.6 Application to a furnace process 278 7.6.1 Process description 278 7.6.2 Description of sensor bias 279 7.6.3 Application of PCA 280 7.6.4 Utilizing MWPCA based on an application delay 282 7.7 Adaptive partial least squares 286 7.7.1 Recursive Adaptation of SX0X0 and Sx0y0 287 7.7.2 Moving Window Adaptation of SX0X0 and Sx0y0 287 7.7.3 Adapting the number of source signals 287 7.7.4 Adaptation of the PLS model 290 7.8 Tutorial Session 292 8 Monitoring changes in covariance structure 293 8.1 Problem analysis 294 8.1.1 First intuitive example 294 8.1.2 Generic statistical analysis 297 8.1.3 Second intuitive example 299 8.2 Preliminary discussion of related techniques 304 8.3 Definition of primary and improved residuals 305 8.3.1 Primary residuals for eigenvectors 306 8.3.2 Primary residuals for eigenvalues 307 8.3.3 Comparing both types of primary residuals 307 8.3.4 Statistical properties of primary residuals 312 8.3.5 Improved residuals for eigenvalues 315 8.4 Revisiting the simulation examples of Section 8.1 317 8.4.1 First simulation example 318 8.4.2 Second simulation example 321 8.5 Fault isolation and identification 324 8.5.1 Diagnosis of step-type fault conditions 325 8.5.2 Diagnosis of general deterministic fault conditions 328 8.5.3 A simulation example 328 8.6 Application study of a gearbox system 331 8.6.1 Process description 332 8.6.2 Fault description 332 8.6.3 Identification of a monitoring model 334 8.6.4 Detecting a fault condition 338 8.7 Analysis of primary and improved residuals 341 8.7.1 Central limit theorem 341 8.7.2 Further statistical properties of primary residuals 344 8.7.3 Sensitivity of statistics based on improved residuals 349 8.8 Tutorial session 353 Part IV Description of Modeling Methods 355 9 Principal component analysis 357 9.1 The core algorithm 357 9.2 Summary of the PCA algorithm 362 9.3 Properties of a PCA model 363 10 Partial least squares 375 10.1 Preliminaries 375 10.2 The core algorithm 377 10.3 Summary of the PLS algorithm 380 10.4 Properties of PLS 381 10.5 Properties of maximum redundancy PLS 396 References 410 Index 427
£62.96
John Wiley & Sons Inc Multivariable Model Building
Book SynopsisMultivariable regression models are of fundamental importance in all areas of science in which empirical data must be analyzed. This book proposes a systematic approach to building such models based on standard principles of statistical modeling. The main emphasis is on the fractional polynomial method for modeling the influence of continuous variables in a multivariable context, a topic for which there is no standard approach. Existing options range from very simple step functions to highly complex adaptive methods such as multivariate splines with many knots and penalisation. This new approach, developed in part by the authors over the last decade, is a compromise which promotes interpretable, comprehensible and transportable models.Trade Review“This new approach, developed in part by the authors over the last decade, is a compromise which promotes interpretable, comprehensible and transportable models.” (Zentralblatt Math, 1 October 2013) “The book is very useful for practicing statisticians and can also be recommended for teaching purposes.” (Biometrical Journal, July 2009) “It is an excellent book on multivariable model-building, presenting the material in an easy-to-understand and informal style.” (Mathematical Reviews, 2009) "This excellent book fills a gap in the current literature on statistical modelling. It is the first time that a book is devoted to the whole breadth of application of fractional polynomials. The authors are the experts on this useful methodology." (Statistics in Medicine, Feb 2009)Table of ContentsPreface. 1. Introduction. 1.1 Real-Life Problems as Motivation for Model Building. 1.2 Issues in Modelling Continuous Predictors. 1.3 Types of Regression Model Considered. 1.4 Role of Residuals. 1.5 Role of Subject-Matter Knowledge in Model Development. 1.6 Scope of Model Building in our Book. 1.7 Modelling Preferences. 1.8 General Notation. 2. Selection of Variables. 2.1 Introduction. 2.2 Background. 2.3 Preliminaries for a Multivariable Analysis. 2.4 Aims of Multivariable Models. 2.5 Prediction: Summary Statistics and Comparisons. 2.6 Procedures for Selecting Variables. 2.7 Comparison of Selection Strategies in Examples. 2.8 Selection and Shrinkage. 2.9 Discussion. 3. Handling Categorical and Continuous Predictors. 3.1 Introduction. 3.2 Types of Predictor. 3.3 Handling Ordinal Predictors. 3.4 Handling Counting and Continuous Predictors: Categorization. 3.5 Example: Issues in Model Building with Categorized Variables. 3.6 Handling Counting and Continuous Predictors: Functional Form. 3.7 Empirical Curve Fitting. 3.8 Discussion. 4. Fractional Polynomials for One Variable. 4.1 Introduction. 4.2 Background. 4.3 Definition and Notation. 4.4 Characteristics. 4.5 Examples of Curve Shapes with FP1 and FP2 Functions. 4.6 Choice of Powers. 4.7 Choice of Origin. 4.8 Model Fitting and Estimation. 4.9 Inference. 4.10 Function Selection Procedure. 4.11 Scaling and Centering. 4.12 FP Powers as Approximations to Continuous Powers. 4.13 Presentation of Fractional Polynomial Functions. 4.14 Worked Example. 4.15 Modelling Covariates with a Spike at Zero. 4.16 Power of Fractional Polynomial Analysis. 4.17 Discussion. 5. Some Issues with Univariate Fractional Polynomial Models. 5.1 Introduction. 5.2 Susceptibility to Influential Covariate Observations. 5.3 A Diagnostic Plot for Influential Points in FP Models. 5.4 Dependence on Choice of Origin. 5.5 Improving Robustness by Preliminary Transformation. 5.6 Improving Fit by Preliminary Transformation. 5.7 Higher Order Fractional Polynomials. 5.8 When Fractional Polynomial Models are Unsuitable. 5.9 Discussion. 6. MFP: Multivariable Model-Building with Fractional Polynomials. 6.1 Introduction. 6.2 Motivation. 6.3 The MFP Algorithm. 6.4 Presenting the Model. 6.5 Model Criticism. 6.6 Further Topics. 6.7 Further Examples. 6.8 Simple Versus Complex Fractional Polynomial Models. 6.9 Discussion. 7. Interactions. 7.1 Introduction. 7.2 Background. 7.3 General Considerations. 7.4 The MFPI Procedure. 7.5 Example 1: Advanced Prostate Cancer. 7.6 Example 2: GBSG Breast Cancer Study. 7.7 Categorization. 7.8 STEPP. 7.9 Example 3: Comparison of STEPP with MFPI. 7.10 Comment on Type I Error of MFPI. 7.11 Continuous-by-Continuous Interactions. 7.12 Multi-Category Variables. 7.13 Discussion. 8. Model Stability. 8.1 Introduction. 8.2 Background. 8.3 Using the Bootstrap to Explore Model Stability. 8.4 Example 1: Glioma Data. 8.5 Example 2: Educational Body-Fat Data. 8.6 Example 3: Breast Cancer Diagnosis. 8.7 Model Stability for Functions. 8.8 Example 4: GBSG Breast Cancer Data. 8.9 Discussion. 9. Some Comparisons of MFP with Splines. 9.1 Introduction. 9.2 Background. 9.3 MVRS: A Procedure for Model Building with Regression Splines. 9.4 MVSS: A Procedure for Model Building with Cubic Smoothing Splines. 9.5 Example 1: Boston Housing Data. 9.6 Example 2: GBSG Breast Cancer Study. 9.7 Example 3: Pima Indians. 9.8 Example 4: PBC. 9.9 Discussion. 10. How To Work with MFP. 10.1 Introduction. 10.2 The Dataset. 10.3 Univariate Analyses. 10.4 MFP Analysis. 10.5 Model Criticism. 10.6 Stability Analysis. 10.7 Final Model. 10.8 Issues to be Aware of . 10.9 Discussion. 11. Special Topics Involving Fractional Polynomials. 11.1 Time-Varying Hazard Ratios in the Cox Model. 11.2 Age-specific Reference Intervals. 11.3 Other Topics. 12. Epilogue. 12.1 Introduction. 12.2 Towards Recommendations for Practice. 12.3 Omitted Topics and Future Directions. 12.4 Conclusion. Appendix A: Data and Software Resources. A.1 Summaries of Datasets. A.2 Datasets used more than once. A.2.1 Research Body Fat. A.2.2 GBSG Breast Cancer. A.2.3 Educational Body Fat. A.2.4 Glioma. A.2.5 Prostate Cancer. A.2.6 Whitehall I. A.2.7 PBC. A.2.8 Oral Cancer. A.2.9 Kidney Cancer. A.3 Software. Appendix B: Glossary of Abbreviations. References. Index
£95.36
John Wiley & Sons Inc Geostatistics for Environmental 2e Statistics in
Book SynopsisThere are many factors that environmental scientists should consider in their research. Weather and climate vary widely between locations, soil varies at every spatial scale at which it is examined, and even man-made attributes, such as the distribution of pollution, fluctuate significantly.Trade Review"This is certainly an invaluable text for advanced undergraduate and graduate students of spatial variation and environmental research." (International Journal of Environmental and Analytical Chemistry, August 2008)Table of ContentsPreface 1 Introduction 2 Basic Statistics 3 Prediction and Interpolation 4 Characterizing Spatial Processes: The Covariance and Variogram 5 Modelling the Variogram 6 Reliability of the Experimental Variogram and Nested Sampling 7 Spectral Analysis 8 Local Estimation or Prediction: Kriging 9 Kriging in the Presence of Trend and Factorial Kriging 10 Cross-Correlation, Coregionalization and Cokriging 11 Disjunctive Kriging 12 Stochastic Simulation (new file) Appendix A Appendix B References Index
£97.16
John Wiley & Sons Inc Uncertain Judgements
Book SynopsisUncertain Judgments Eliciting Experts' Probabilities presents a range of tried and tested elicitation methods to enable statisticians to get make the most of expert opinion. An elicitation method forms a bridge between an expert's opinion and an expression of these points in a statistically useful form.Trade Review“This book, written by a group of expert statisticians and psychologists, provides an introduction to the subject and a detailed overview of the existing literature. The book guides the reader through the design of an elicitation method and details examples from a cross section of literature in the statistics, psychology, engineering and health sciences disciplines.” (Zentralblatt Math, 1 August 2013) "This is an interesting, well-written book that will be valuable to any decision maker who much rely on expert judgments, any statistician who uses Bayesian statistics, and any researcher who wishes to understand the field of elicitation." (Journal of the American Statistical Association, March 2009) "This book provides an excellent introduction and working reference to the subject of its title and should be an invaluable aid to producers and consumers of expert opinion." (Biometrics, September 2008) "I recommend 'Uncertain Judgements' as an excellent source for a wide variety of research." (Psychometrika, March 2008) “…will be of interest to those who are concerned with or interested primarily in the practicalities of modeling expert judgement and opinion.” (International Journal of Marketing, January 2007)Table of ContentsPreface xi 1 Fundamentals of Probability and Judgement 1 1.1 Introduction 1 1.2 Probability and elicitation 1 1.2.1 Probability 1 1.2.2 Random variables and probability distributions 3 1.2.3 Summaries of distributions 5 1.2.4 Joint distributions 7 1.2.5 Bayes’ Theorem 8 1.2.6 Elicitation 9 1.3 Uncertainty and the interpretation of probability 10 1.3.1 Aleatory and epistemic uncertainty 10 1.3.2 Frequency and personal probabilities 11 1.3.3 An extended example 12 1.3.4 Implications for elicitation 14 1.4 Elicitation and the psychology of judgement 14 1.4.1 Judgement – absolute or relative? 15 1.4.2 Beyond perception 18 1.4.3 Implications for elicitation 20 1.5 Of what use are such judgements? 20 1.5.1 Normative theories of probability 21 1.5.2 Coherence 21 1.5.3 Do elicited probabilities have the desired interpretation? 22 1.6 Conclusions 24 1.6.1 Elicitation practice 24 1.6.2 Research questions 24 2 The Elicitation Context 25 2.1 How and who? 25 2.1.1 Choice of format 25 2.1.2 What is an expert? 26 2.2 The elicitation process 27 2.2.1 Roles within the elicitation process 28 2.2.2 A model for the elicitation process 28 2.3 Conventions in Chapters 3 to 9 31 2.4 Conclusions 31 2.4.1 Elicitation practice 31 2.4.2 Research question 31 3 The Psychology of Judgement Under Uncertainty 33 3.1 Introduction 33 3.1.1 Why psychology? 33 3.1.2 Chapter overview 34 3.2 Understanding the task and the expert 35 3.2.1 Cognitive capabilities: the proper view of human information processing? 35 3.2.2 Constructive processes: the proper view of the process? 36 3.3 Understanding research on human judgement 37 3.3.1 Experts versus the rest: the proper focus of research? 37 3.3.2 Early research on subjective probability: ‘conservatism’ in Bayesian probability revision 38 3.4 The heuristics and biases research programme 38 3.4.1 Availability 39 3.4.2 Representativeness 41 3.4.3 Do frequency representations remove the biases attributed to availability and representativeness? 46 3.4.4 Anchoring-and-adjusting 47 3.4.5 Support theory 49 3.4.6 The affect heuristic 51 3.4.7 Critique of the heuristics and biases approach 52 3.5 Experts and expertise 52 3.5.1 The heuristics and biases approach 53 3.5.2 The cognitive science approach 53 3.5.3 ‘The middle way’ 54 3.6 Three meta-theories of judgement 55 3.6.1 The cognitive continuum 56 3.6.2 The inside versus the outside view 56 3.6.3 The naive intuitive statistician metaphor 58 3.7 Conclusions 58 3.7.1 Elicitation practice 58 3.7.2 Research questions 59 4 The Elicitation of Probabilities 61 4.1 Introduction 61 4.2 The calibration of subjective probabilities 62 4.2.1 Research methods in calibration research 67 4.2.2 Calibration research: general findings 68 4.2.3 Calibration research in applied settings 72 4.2.4 A case study in probability judgement: calibration research in medicine 74 4.3 The calibration of subjective probabilities: theories and explanations 77 4.3.1 Explanations of probability judgement in calibration tasks 77 4.3.2 Theories of the calibration of subjective probabilities 79 4.4 Representations and methods 82 4.4.1 Different modes for representing uncertainty 83 4.4.2 Different formats for eliciting responses 87 4.4.3 Key lessons 89 4.5 Debiasing 89 4.5.1 General principles for debiasing judgement 90 4.5.2 Managing noise 91 4.5.3 Redressing insufficient regressiveness in prediction 92 4.5.4 A caveat concerning post hoc corrections 94 4.6 Conclusions 95 4.6.1 Elicitation practice 95 4.6.2 Research questions 95 5 Eliciting Distributions – General 97 5.1 From probabilities to distributions 97 5.1.1 From a few to infinity 98 5.1.2 Summaries 99 5.1.3 Fitting 100 5.1.4 Overview 100 5.2 Eliciting univariate distributions 100 5.2.1 Summaries based on probabilities 100 5.2.2 Proportions 104 5.2.3 Other summaries 105 5.3 Eliciting multivariate distributions 107 5.3.1 Structuring 107 5.3.2 Eliciting association 108 5.3.3 Joint and conditional probabilities 111 5.3.4 Regression 112 5.3.5 Many variables 113 5.4 Uncertainty and imprecision 114 5.4.1 Quantifying elicitation error 114 5.4.2 Sensitivity analysis 115 5.4.3 Feedback and overfitting 116 5.5 Conclusions 118 5.5.1 Elicitation practice 118 5.5.2 Research questions 119 6 Eliciting and Fitting a Parametric Distribution 121 6.1 Introduction 121 6.2 Outline of this chapter 122 6.3 Eliciting opinion about a proportion 124 6.4 Eliciting opinion about a general scalar quantity 132 6.5 Eliciting opinion about a set of proportions 137 6.6 Eliciting opinion about the parameters of a multivariate normal distribution 139 6.7 Eliciting opinion about the parameters of a linear regression model 142 6.8 Eliciting opinion about the parameters of a generalised linear model 145 6.9 Elicitation methods for other problems 147 6.10 Deficiencies in existing research 149 6.11 Conclusions 150 6.11.1 Elicitation practice 150 6.11.2 Research questions 151 7 Eliciting Distributions – Uncertainty and Imprecision 153 7.1 Introduction 153 7.2 Imprecise probabilities 153 7.3 Incomplete information 156 7.4 Summary 160 7.5 Conclusions 160 7.5.1 Elicitation practice 160 7.5.2 Research questions 160 8 Evaluating Elicitation 161 8.1 Introduction 161 8.1.1 Good elicitation 161 8.1.2 Inaccurate knowledge 161 8.1.3 Automatic calibration 162 8.1.4 Lessons of the psychological literature 163 8.1.5 Outline of this chapter 163 8.2 Scoring rules 163 8.2.1 Scoring rules for discrete probability distributions 165 8.2.2 Scoring rules for continuous probability distributions 169 8.3 Coherence, feedback and overfitting 171 8.3.1 Coherence and calibration 171 8.3.2 Feedback and overfitting 173 8.4 Conclusions 176 8.4.1 Elicitation practice 176 8.4.2 Research questions 177 9 Multiple Experts 179 9.1 Introduction 179 9.2 Mathematical aggregation 180 9.2.1 Bayesian methods 180 9.2.2 Opinion pooling 181 9.2.3 Cooke’s method 184 9.2.4 Performance of mathematical aggregation 185 9.3 Behavioural aggregation 186 9.3.1 Group elicitation 186 9.3.2 Other methods of behavioural aggregation 188 9.3.3 Performance of behavioural methods 190 9.4 Discussion 190 9.5 Elicitation practice 191 9.6 Research questions 191 10 Published Examples of the Formal Elicitation of Expert Opinion 193 10.1 Some applications 193 10.2 An example of an elicitation interview – eliciting engine sales 193 10.3 Medicine 195 10.3.1 Diagnosis and treatment decisions 195 10.3.2 Clinical trials 199 10.3.3 Survival analysis 201 10.3.4 Clinical psychology 202 10.4 The nuclear industry 204 10.5 Veterinary science 206 10.6 Agriculture 207 10.7 Meteorology 208 10.8 Business studies, economics and finance 209 10.9 Other professions 212 10.10 Other examples of the elicitation of subjective probabilities 213 11 Guidance on Best Practice 217 12 Areas for Research 223 Glossary 227 Bibliography 267 Author Index 307 Index 313
£57.90
John Wiley & Sons Inc Digital Control
Book SynopsisDigital control systems are becoming increasingly prevalent and important within industry. In recent years significant progress has been made in their analysis and design - particularly within the areas of microprocessors and digital signal processors.Table of ContentsPreface. Acknowledgements. List of Matlab Code. List of Acronyms. 1. Introduction. 2. Modelling of Sampled Data Systems. I: Digital Signal Processing. 3. Linear System. 4. Z-Transform. 5. Frequency Domain Analysis. II: Identification. 6. Identification. III: Transfer Function Approach to Controller Design. 7. Structures and Specifications. 8. Proportional, Integral, Derivative Controllers. 9. Pole Placement Controllers. 10. Special Cases of Pole Placement Control. 11. Minimum Variance Control. 12. Model Predictive Control. 13. Linear Quadratic Gaussian Control. IV: State Space Approach to controller Design. 14. State Space Techniques in Controller Design. Appendix A. Supplementary Material. References. Index. Index of Matlab Code.
£58.85
John Wiley & Sons Inc Hydrodynamics of Free Surface Flows Modelling
Book SynopsisA definitive guide for accurate state-of-the-art modelling of free surface flows Understanding the dynamics of free surface flows is the starting point of many environmental studies, impact studies, and waterworks design.Trade Review?The book gains an insight into the mathematical fundament of free surface flows and into the implementation of these models in the programme system Telemac. It is useful for students and researchers of this field and of computational fluid dynamics.? (ZAMM, October 2009) "This would provide a useful guide from fundamental theory to more advanced topics that deal with the applications of the finite element method and the Telemac system." (Zentralblatt Math 1131, June 2008)Table of ContentsList of Figures. List of Tables. List of Plates. Acknowledgements. Chapter 1. Acknowledgements. Chapter 2. Equations of free surface hydrodynamics. Chapter 3. Principles of the finite element method. Chapter 4. Resolution of the Saint-Venant equations. Chapter 5. Resolution of the Navier-Stokes equations. Chapter 6. Solving transport equations. Chapter 7. Modern techniques in finite elements. Chapter 8. Parallelism. Chapter 9. Parameter estimation. Chapter 10. Applications. Appendix A. Tide-generating force. Appendix B. Diffusion matrix with tetrahedra. Appendix C. Notations. Bibliography. Index.
£999.99
John Wiley & Sons Inc Linear Models for Unbalanced Data
Book SynopsisWILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation.Trade Review"…I would recommend this book to undergraduate students as well as graduates." (MAA Reviews, January 28, 2008)Table of Contents1. An Up-Dated Viewpoint: Cell Means Models. 2. Basic Results for Cell Means Models: The 1-Way Classification. 3. Nested Classifications. 4. The 2-Way Crossed Classification with All-Cells-Filled Data: Cell Means Models. 5. The 2-Way Classification with Some-Cell Empty Data: Cell Means Models. 6. Models with Covariables (Analysis of Covariance): the 1-Way Classification. 7. Matrix Algebra and Quadratic Forms ( A Prelude to Chapter 8). 8. A General Linear Model. 9. The 2-Way Crossed Classification: Overparameterized Models. 10. Extended Cell Means Models. 11. Models with Covariables: The General Case and Some Applications. 12. Comments on Computing Packages. 13. Mixed Models: A Thumbnail Survey. References. Statistical Tables. List of Tables and Figures. Index.
£114.26
John Wiley & Sons Inc Exploring Data Tables Trends and Shapes
Book SynopsisWILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. Exploring Data Tables, Trends, and Shapes (EDTTS) was written as a companion volume to the same editors'' book, Understanding Robust and Exploratory Data Analysis (UREDA). Whereas UREDA is a collection of exploratory and resistant methods of estimation and display, EDTTS goes a step further, describing multivariate and more complicated techniques . . . I feel that the authors have made a very significant contribution in the area of multivariate nonparametric methods. This book [is] a valuable source of reference to researchers in the area. TechnomeTable of Contents1. Theories of Data Analysis: From Magical Thinking Through Classical Statistics 1 Peris Diaconis 1A. Intuitive Statistics—Some Inferential Problems 4 IB. Multiplicity—A Pervasive Problem 9 1C. Some Remedies 12 ID. Theories for Data Analysis 22 IE. Uses for Mathematics 29 IF. In Defense of Controlled Magical Thinking 31 2. Fitting by Organized Comparisons: The Square Combining Table 37 Katherine Godfrey 2A. Combining Comparisons 37 2B. Two-Way Tables 39 2C. Paired Comparisons 47 2D. Analyzing Tables Containing Holes 49 2E. Summary 61 3. Resistant Nonadditive Fits for Two-Way Tables 67 John D. Emerson and Gregory Y. Wong 3A. The Simple Additive Model and Median Polish 68 3B. One Step Beyond an Additive Fit 71 3C. Assessing and Comparing Fits 79 3D. Multiplicative Fits 83 3E. Techniques for Obtaining Simple Multiplicative Fits 92 3F. Additive-Plus-Multiplicative Fits 100 3G. Some Background for Nonadditive Fits 113 3H. Summary 117 4. Three-Way Analysis 125 Nancy Cook 4A. Structure of the Three-Way Table 126 4B. Decompositions and Models for Three-Way Analysis 128 4C. Median-Polish Analysis for the Main-Effects-Only Case 130 4D. Nonadditivity and a Diagnostic Plot in Main-Effects-Only Analysis 145 4E. Analysis Using Means 158 4F. Median-Polish Analysis for the Full-Effects Case 164 4G. Diagnostic Plots for the Full-Effects Case 176 4H. Fitting the Full-Effects Model by Means 180 4I. Computation, Other Polishes, and Missing Values 182 4J. Summary 183 5. Identifying Extreme Cells in a Sizable Contingency Table: Probabilistic and Exploratory Approaches 189 Frederick Mosteller and Anita Parunak 5A. The Hypergeometric Distribution 192 5B. Assessing Outliers 195 5C. The Simulation Approach 199 5D. Applying the Simulation Approach to the Table of Archaeological Data 206 5E. An Exploratory Approach, Based on Deviations from Independence 212 5F. A Logarithmic Exploratory Approach 214 5G. Illustrations of the New Standardization 217 5H. Summary 221 51. Conclusion 223 6. Fitting Straight Lines By Eye 225 Frederick Mosteller, Andrew F. Siegel, Edward Trapido, and Cleo Youtz 6A. Method 226 6B. Results 229 6C. Summary 238 7. Resistant Multiple Regression, One Variable at a Time 241 John D. Emerson and David C. Hoaglin 7A. Resistant Lines 242 7B. Sweeping Out 246 7C. Example 250 7D. When Carriers Come in Blocks 263 7E. Summary 273 8. Robust Regression 281 Guoying Li 8A. Why Robust Regression? 282 8B. M-Estimators and W-Estimators for Regression 291 8C. Computation 304 8D. Example: The Stack Loss Data 310 8E. Bounded-Influence Regression 322 8F. Some Alternative Methods 328 8G. Summary 335 9. Checking the Shape of Discrete Distributions 345 David C. Hoaglin and John W. Tukey 9A. A Poissonness Plot 348 9B. Confidence Intervals for the Count Metameter 358 9C. When Is a Point Discrepant? 370 9D. Overall Plots for Other Families of Distributions 376 9E. Frequency-Ratio Alternatives 389 9F. Cooperative Diversity 396 9G. Double-Root Residuals 406 9H. Summary 409 10. Using Quantiles to Study Shape 417 David C. Hoaglin 10A. Diagnosing Skewness 419 10B. Diagnosing Elongation 425 IOC. Quantile-Quantile Plots 432 10D. Plots for Skewness and Elongation 442 10E. Pushback Analysis 450 10F. Summary 454 10G. Appendix 456 11. Summarizing Shape Numerically: The g-and-h Distributions 416 David C. Hoaglin 11 A. Skewness 462 11B. Elongation 479 11C. Combining Skewness and Elongation 485 11D. More General Patterns of Skewness and Elongation 490 HE. Working from Frequency Distributions 496 11F. Moments 501 11G. Other Approaches to Shape 504 11H. Summary 508 Index.
£110.66
John Wiley & Sons Inc Sampling of Populations
Book SynopsisA trusted classic on the key methods in population samplingnow in a modernized and expanded new edition Sampling of Populations, Fourth Edition continues to serve as an all-inclusive resource on the basic and most current practices in population sampling. Maintaining the clear and accessible style of the previous edition, this book outlines the essential statistical methodsfor survey design and analysis, while also exploring techniques that have developed over the past decade. The Fourth Edition successfully guides the reader through the basic concepts and procedures that accompany real-world sample surveys, such as sampling designs, problems of missing data, statistical analysis of multistage sampling data, and nonresponse and poststratification adjustment procedures. Rather than employ a heavily mathematical approach, the authors present illustrative examples that demonstrate the rationale behind common steps in the sampling process, from creating effeTrade Review“The book remains a very appropriately written text for classroom use, especially for students studying public health or epidemiology, or for undergraduate majors in statistics and related fields.” (Biometrics, June 2009)Table of ContentsTables. Boxes. Figures. Getting Files from the Wiley ftp and Internet Sites. List of Data Sites Provides on Web Site. Preface to the Fourth Edition. Part 1: Basic Concepts. 1. Use of Sample Surveys. 2. The Population and the Sample. Part 2: Major Sampling Designs and Estimation Procedures. 3. Simple Random Sampling. 4. Systematic Sampling. 5. Stratification and Stratified Random Sampling. 6. Stratified Random Sampling: Further Issues. 7. Ratio Estimation. 8. Cluster Sampling: Introduction and Overview. 9. Simple One-Stage Cluster Sampling. 10. Two-Stage Cluster Sampling: Clusters Sampled with Equal Probability. 11. Cluster Sampling in Which Clusters Are Sampled with Unequal Probability: Probability Proportional to Size Sampling. 12. Variance Estimation in Complex Sample Surveys. Part 3: Selected Topics in Sample Survey Methodology. 13. Nonresponse and Missing Data in Sample Surveys. 14. Selected Topics in Sample Design and Estimation Methodology. 15. Telephone Survey Sampling (Michael W. Link and Mansour Fahimi). 16. Constructing the Survey Weights (Paul P. Biemer and Sharon L. Christ). 17. Strategies for Design-Based Analysis of Sample Survey Data. Appendix. Answers to Selected Exercises. Index.
£132.26
John Wiley & Sons Inc Theorems Corollaries Lemmas and Methods of Proof
Book SynopsisThe primary purpose of this text is to introduce math majors, who have completed a calculus sequence, to the axiomatic makeup of modern mathematics. Heavy emphasis is placed on the writing of clear and understandable proofs.Trade Review"this book can be very useful for students in their work" (Zentralblatt MATH, 11th April 2007)Table of ContentsPreface. Chapter 1. Introduction to Modern Mathematics. Chapter 2. An Introduction to Symbolic Logic. Chapter 3. Methods of Proof. Chapter 4. Introduction to Number Theory. Chapter 5. The Foundations of Calculus. Chapter 6. Foundations of Algebra. References. Index.
£116.96
