Probability and statistics Books
Springer-Verlag New York Inc. Mixed Effects Models and Extensions in Ecology
Book SynopsisLimitations of Linear Regression Applied on Ecological Data.- Things are not Always Linear; Additive Modelling.- Dealing with Heterogeneity.- Mixed Effects Modelling for Nested Data.- Violation of Independence Part I.- Violation of Independence Part II.- Meet the Exponential Family.- GLM and GAM for Count Data.- GLM and GAM for AbsencePresence and Proportional Data.- Zero-Truncated and Zero-Inflated Models for Count Data.- Generalised Estimation Equations.- GLMM and GAMM.- Estimating Trends for Antarctic Birds in Relation to Climate Change.- Large-Scale Impacts of Land-Use Change in a Scottish Farming Catchment.- Negative Binomial GAM and GAMM to Analyse Amphibian Roadkills.- Additive Mixed Modelling Applied on Deep-Sea Pelagic Bioluminescent Organisms.- Additive Mixed Modelling Applied on Phytoplankton Time Series Data.- Mixed Effects Modelling Applied on American Foulbrood Affecting Honey Bees Larvae.- Three-Way Nested Data for Age Determination Techniques Applied to Cetaceans.- GLTrade ReviewFrom the reviews:"For many people dealing with statistics is like jumping into ice-cold water. This metaphor is depicted by the cover of this book … . full of excellent example code and for most graphs and analyses the code is printed and explained in detail. … Each example finishes with … valuable information for a person new to a technique. In summary, I highly recommend the book to anyone who is familiar with basic statistics … who wants to expand his/her statistical knowledge to analyse ecological data." (Bernd Gruber, Basic and Applied Ecology, Vol. 10, 2009)"This book is written in a very approachable conversational style. The additional focus on the heuristics of the process rather than just a rote recital of theory and equations is commendable. This type of approach helps the reader get behind the ‘why’ of what’s being done rather than blindly follow a simple list of rules.… In short, this text is good for researchers with at least a little familiarity with the basic concepts of modeling and who want some solid stop-by-stop guidance with examples on how common ecological modeling tasks are accomplished using R." (Aaron Christ, Journal of Statistical Software, November 2009, Vol. 32)"The authors succeed in explaining complex extensions of regression in largely nonmathematical terms and clearly present appropriate R code for each analysis. A major strength of the text is that instead of relying on idealized datasets … the authors use data from consulting projects or dissertation research to expose issues associated with ‘real’ data. … The book is well written and accessible … . the volume should be a useful reference for advanced graduate students, postdoctoral researchers, and experienced professionals working in the biological sciences." (Paul E. Bourdeau, The Quarterly Review of Biology, Vol. 84, December, 2009)“This is a companion volume to Analyzing Ecology Data by the same authors. …It extends the previous work by looking at more complex general and generalized linear models involving mixed effects or heterogeneity in variances. It is aimed at statistically sophisticated readers who have a good understanding of multiple regression models… .The pedagogical style is informal… . The authors are pragmatists—they use combinations of informal graphical approaches, formal hypothesis testing, and information-theoretical model selection methods when analyzing data. …Advanced graduate students in ecology or ecologists with several years of experience with ‘messy’ data would find this book useful. …Statisticians would find this book interesting for the nice explorations of many of the issues with messy data. This book would be (very) suitable for a graduate course on statistical consulting—indeed, students would learn a great deal about the use of sophisticated statistical models in ecology! …I very much liked this book (and also the previous volume). I enjoyed the nontechnical presentations of the complex ideas and their emphasis that a good analysis uses ‘simple statistical methods wherever possible, but doesn’t use them simplistically.’” (Biometrics, Summer 2009, 65, 992–993)“This book is a great introduction to a wide variety of regression models. … This text examines how to fit many alternative models using the statistical package R. … The text is a valuable reference … . A large number of real datasets are used as examples. Discussion on which model to use and the large number of recent references make the book useful for self study … .” (David J. Olive, Technometrics, Vol. 52 (4), November, 2010)Table of ContentsLimitations of linear regression applied on ecological data. - Things are not always linear; additive modelling. - Dealing with hetergeneity. - Mixed modelling for nested data. - Violation of independence - temporal data. - Violation of independence; spatial data. - Generalised linear modelling and generalised additive modelling. - Generalised estimation equations. - GLMM and GAMM. - Estimating trends for Antarctic birds in relation to climate change. - Large-scale impacts of land-use change in a Scottish farming catchment. - Negative binomial GAM and GAMM to analyse amphibian road killings. - Additive mixed modelling applied on deep-sea plagic bioluminescent organisms. - Additive mixed modelling applied on phyoplankton time series data. - Mixed modelling applied on American Fouldbrood affecting honey bees larvae. - Three-way nested data for age determination techniques applied to small cetaceans. - GLMM applied on the spatial distribution of koalas in a fragmented landscape. - GEE and GLMM applied on binomial Badger activity data.
£113.99
Springer Explorations in Monte Carlo Methods
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£44.99
Springer Introductory Time Series with R
Book SynopsisOnce the model has been introduced it is used to generate synthetic data, using R code, and these generated data are then used to estimate its parameters. This sequence enhances understanding of both the time series model and the R function used to fit the model to data.Trade ReviewFrom the reviews:“The book…gives a very broad and practical overview of the most common models for time series analysis in the time domain and in the frequency domain, with emphasis on how to implement them with base R and existing R packages such as Rnlme, MASS, tseries, fracdiff, mvtnorm, vars, and sspir. The authors explain the models by first giving a basic theoretical introduction followed by simulation of data from a particular model and fitting the latter to the simulated data to recover the parameters. After that, they fit the class of models to either environmental, finance, economics, or physics data. There are many applications to climate change and oceanography. The R programs for the simulations are given even if there are R functions that would do the simulation. All examples given can be reproduced by the reader using the code provided…in all chapters. Exercises at the end of each chapter are interesting, involving simulation, estimation, description, graphical analysis, and some theory. Data sets used throughout the book are available in a web site or come with base R or the R packages used. The book is a great guide to those wishing to get a basic introduction to modern time series modeling in practice, and in a short amount of time. …” (Journal of Statistical Software, January 2010, Vol. 32, Book Review 4)“Later year undergraduates, beginning graduate students, and researchers and graduate students in any discipline needing to explore and analyse time series data. This very readable text covers a wide range of time series topics, always however within a theoretical framework that makes normality assumptions. The range of models that are discussed is unusually wide for an introductory text. … The mathematical theory is remarkably complete … . This text is recommended for its wide-ranging and insightful coverage of time series theory and practice.” (John H. Maindonald, International Statistical Review, Vol. 78 (3), 2010)“The authors present a textbook for students and applied researchers for time series analysis and linear regression analysis using R as the programming and command language. … The book is written for students with knowledge of a first-year university statistics course in New-Zealand and Australia, but it also might serve as a useful tools for applied researchers interested in empirical procedures and applications which are not menu driven as it is the case for most econometric software packages nowadays.” (Herbert S. Buscher, Zentralblatt MATH, Vol. 1179, 2010)Table of ContentsTime Series Data.- Correlation.- Forecasting Strategies.- Basic Stochastic Models.- Regression.- Stationary Models.- Non-stationary Models.- Long-Memory Processes.- Spectral Analysis.- System Identification.- Multivariate Models.- State Space Models.
£49.99
Springer Applied Statistical Genetics with R
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£59.99
Springer Finite Markov Chains
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£71.99
Springer-Verlag New York Inc. The Mathematics of Time Essays On Dynamical
Book SynopsisDifferentiable Dynamical Systems.- Notes.- References for Notes.- What Is Global Analysis?.- Stability and Genericity in Dynamical Systems.- Personal Perspectives on Mathematics and Mechanics.- Dynamics in General Equilibrium Theory.- Some Dynamical Questions in Mathematical Economics.- Review of Global Variational Analysis: Weier strass Integrals on a Riemannian Manifold.- Review of Catastrophe Theory: Selected Papers.- On the Problem of Reviving the Ergodic Hypothesis of Boltzmann and Birkhoff.- Robert Edward Bowen (jointly with J. Feldman and M. Ratner).- On How I Got Started in Dynamical Systems.Table of ContentsDifferentiable Dynamical Systems.- Notes.- References for Notes.- What Is Global Analysis?.- Stability and Genericity in Dynamical Systems.- Personal Perspectives on Mathematics and Mechanics.- Dynamics in General Equilibrium Theory.- Some Dynamical Questions in Mathematical Economics.- Review of Global Variational Analysis: Weier strass Integrals on a Riemannian Manifold.- Review of Catastrophe Theory: Selected Papers.- On the Problem of Reviving the Ergodic Hypothesis of Boltzmann and Birkhoff.- Robert Edward Bowen (jointly with J. Feldman and M. Ratner).- On How I Got Started in Dynamical Systems.
£66.49
Springer Bayesian Computation with R
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£62.99
Springer-Verlag New York Inc. A Beginners Guide to R
Book SynopsisGetting Data into R.- Accessing Variables and Managing Subsets of Data.- Simple Functions.- An Introduction to Basic Plotting Tools.- Loops and Functions.- Graphing Tools.- An Introduction to the Lattice Package.- Common R Mistakes.Trade ReviewFrom the reviews:“A Beginner’s Guide to R is just what its title implies, a quick-start guide for the newest R users. A unique feature of this welcome addition to Springer’s Use R! series is that it is devoted solely to getting the user up and running on R. Unlike other texts geared towards R beginners, …this text does not make the mistake of trying to simultaneously teach statistics. …there are straightforward homework exercises provided throughout…, and the data sets can be downloaded from the authors’ website… …A Beginner’s Guide to R is an essential resource for the R novice, whether an undergraduate learning statistics for the first time or a seasoned statistician biting the bullet and making the switch to R. “ (The R Journal Vol. 2/1, June 2010)“…most suitable for an advanced beginner or a user who needs an introduction to a wide variety of graphical methods. Overall, the book does most things quite well. It shows the beginner how to install R. how to load data into R, how to perform some subsetting operations including the sorting of data and most of all how to plot data using a variety of methods. Throughout, all methods and code are will illustrated and can be easily replicated by anyone using the book. …I learned quite a number of things about R that I did not previously know. Consequently, I would recommend the book not only for the students who need to learn R, but for professionals who need to enhance their basic working knowledge of R." (Math Geosci 2010, 42: 133–137)“The book has many admirable features. It introduces key commands in easy stages. Each chapter has a number of illustrative examples, lucidly explained, and ends with a review of what has been covered. Chapters also contain exercises at the end that reinforce the examples provided. … useful work for self-study or for an introductory course, allowing readers to apply their knowledge of the language to begin learning how to use R for statistical analysis or other purposes. Summing Up: Highly recommended. All levels of readership.” (R. Bharath, Choice, Vol. 47 (11), July, 2010)“This book explains how to create datasets, variables, functions and plots using R. It is not a simple book though. … somewhat dense and covers each topic thoroughly. … best to follow every example. … I found this book to be well written for its intended audience and purpose. I had no difficulty reading it or following the examples. … This approach will give you a good foundation for using R in your own work and advancing to other books about specific analyses and procedures.” (Mark Bailey, Technometrics, Vol. 53 (1), February, 2011)“This book has a very clear objective. … this is a popular book about the R statistical software. … The book is true to its goal of being a text for the absolute beginner with easy to follow explanations, examples to program, and exercises to build skill. The reader who takes advantages of the available data files and R text editors will find this to be a very instructive book. It will definitely increase your desire to learn and use R in the future.” (Brandon Alleman, The American Statistician, May, 2011)Table of ContentsGetting Data into R.- Accessing Variables and Managing Subsets of Data.- Simple Functions.- An Introduction to Basic Plotting Tools.- Loops and Functions.- Graphing Tools.- An Introduction to the Lattice Package.- Common R Mistakes.
£66.49
Springer Stochastic Visibility in Random Fields 95 Lecture Notes in Statistics
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£95.95
Springer The Pleasures of Probability
Book Synopsis1: Cars, Goats, and Sample Spaces. 2: How to Count: Birthdays andLotteries. 3: Conditional Probability: From Kings to Prisoners. 4: TheFormula of Thomas Bayes and Other Matters. 5: The Idea ofIndependence, with Applications. 6: A Little Bit About Games. 7:Random Variables, Expectations, and More About Games. 8: BaseballCards, The Law of Large Numbers, and Bad News for Gamblers. 9: FromTraffic to Chocolate Chip Cookies with the Poisson Distribution. 10:The Desperate Case of the Gambler's Ruin. 11: Breaking Sticks, TossingNeedles, and More: Probability on Continuous Sample Spaces. 12: NormalDistribution, and Order from Diversity via the Central Limit Theorem.13: Random Numbers: What They Are and How to Use Them. 14: Computersand Probability. 15: Statistics: Applying Probability to MakeDecisions. 16: Roaming the Number Line with a Markov Chain:Dependence. 17: The Brownian Motion, and Other Processes in ContinuousTime.Table of Contents1 Cars, Goats, and Sample Spaces.- 1.1 Getting your goat.- 1.2 Nutshell history and philosophy lesson.- 1.3 Let those dice roll. Sample spaces.- 1.4 Discrete sample spaces. Probability distributions and spaces.- 1.5 The car-goat problem solved.- 1.6 Exercises for Chapter 1.- 2 How to Count: Birthdays and Lotteries.- 2.1 Counting your birthdays.- 2.2 Following your dreams in Lottoland.- 2.3 Exercises for Chapter 2.- 3 Conditional Probability: From Kings to Prisoners.- 3.1 Some probability rules. Conditional Probability.- 3.2 Does the king have a sister?.- 3.3 The prisoner’s dilemma.- 3.4 All about urns.- 3.5 Exercises for Chapter 3.- 4. The Formula of Thomas Bayes and Other Matters.- 4.1 On blood tests and Bayes’s formula.- 4.2 An urn problem.- 4.3 Laplace’s law of succession.- 4.4 Subjective probability.- 4.5 Questions of paternity.- 4.6 Exercises for Chapter 4.- 5 The Idea of Independence, with Applications.- 5.1 Independence of events.- 5.2 Waiting for the first head to show.- 5.3 On the likelihood of alien life.- 5.4 The monkey at the typewriter.- 5.5 Rare events do occur.- 5.6 Rare versus extraordinary events.- 5.7 Exercises for Chapter 5.- 6 A Little Bit About Games.- 6.1 The problem of points.- 6.2 Craps.- 6.3 Roulette.- 6.4 What are the odds?.- 6.5 Exercises for Chapter 6.- 7 Random Variables, Expectations, and More About Games.- 7.1 Random variables.- 7.2 The binomial random variable.- 7.3 The game of chuck-a-luck and de Méré’s problem of dice.- 7.4 The expectation of a random variable.- 7.5 Fair and unfair games.- 7.6 Gambling systems.- 7.7 Administering a blood test.- 7.8 Exercises for Chapter 7.- 8 Baseball Cards, The Law of Large Numbers, and Bad News for Gamblers.- 8.1 The coupon collector’s problem.- 8.2 Indicator variables and the expectation of a binomial variable.- 8.3 Independent random variables.- 8.4 The coupon collector’s problem solved.- 8.5 The Law of Large Numbers.- 8.6 The Law of Large Numbers and gambling.- 8.7 A gambler’s fallacy.- 8.8 The variance of a random variable.- 8.8.1 Appendix.- 8.8.2 The variance of the sum of independent random variables.- 8.8.3 The variance ofSn/n.- 8.9 Exercises for Chapter 8.- 9 From Traffic to Chocolate Chip Cookies with the Poisson Distribution.- 9.1 A traffic problem.- 9.2 The Poisson as an approximation to the binomial.- 9.3 Applications of the Poisson distribution.- 9.4 The Poisson process.- 9.5 Exercises for Chapter 9.- 10 The Desperate Case of the Gambler’s Ruin.- 10.1 Let’s go for a random walk.- 10.2 The gambler’s ruin problem.- 10.3 Bold play or timid play?.- 10.4 Exercises for Chapter 10.- 11 Breaking Sticks, Tossing Needles, and More: Probability on Continuous Sample Spaces.- 11.1 Choosing a number at random from an interval.- 11.2 Bus stop.- 11.3 The expectation of a continuous random variable.- 11.4 Normal numbers.- 11.5 Bertrand’s paradox.- 11.6 When do we have a triangle?.- 11.7 Buffon’s needle problem.- 11.8 Exercises for Chapter 11.- 12 Normal Distributions, and Order from Diversity via the Central Limit Theorem.- 12.1 Making sense of some data.- 12.2 The normal distributions.- 12.3 Some pleasant properties of normal distributions.- 12.4 The Central Limit Theorem.- 12.5 How many heads did you get?.- 12.6 Why so many quantities may be approximately normal.- 12.7 Exercises for Chapter 12.- 13 Random Numbers: What They Are and How to Use Them.- 13.1 What are random numbers?.- 13.2 When are digits random? Statistical randomness.- 13.3 Pseudo-random numbers.- 13.4 Random sequences arising from decimal expansions.- 13.5 The use of random numbers.- 13.6 The 1970 draft lottery.- 13.7 Exercises for Chapter 13.- 14 Computers and Probability.- 14.1 A little bit about computers.- 14.2 Frequency of zeros in a random sequence.- 14.3 Simulation of tossing a coin.- 14.4 Simulation of rolling a pair of dice.- 14.5 Simulation of the Buffon needle tosses.- 14.6 Monte Carlo estimate of ? using bombardment of a circle.- 14.7 Monte Carlo estimate for the broken stick problem.- 14.8 Monte Carlo estimate of a binomial probability.- 14.9 Monte Carlo estimate of the probability of winning at craps.- 14.10 Monte Carlo estimate of the gambler’s ruin probability.- 14.11 Constructing approximately normal random variables.- 14.12 Exercises for Chapter 14.- 15 Statistics: Applying Probability to Make Decisions.- 15.1 What statistics does.- 15.2 Lying with statistics?.- 15.3 Deciding between two probabilities.- 15.4 More complicated decisions.- 15.5 How many fish in the lake, and other problems of estimation.- 15.6 Polls and confidence intervals.- 15.7 Random sampling.- 15.8 Some concluding remarks.- 15.9 Exercises for Chapter 15.- 16 Roaming the Number Line with a Markov Chain: Dependence.- 16.1 A picnic in Alphaville?.- 16.2 One-dimensional random walks.- 16.3 The probability of ever returning “home”.- 16.4 About the gambler recouping her losses.- 16.5 The dying out of family names.- 16.6 The number of parties waiting for a taxi.- 16.7 Stationary distributions.- 16.8 Applications to genetics.- 16.9 Exercises for Chapter 16.- 17 The Brownian Motion, and Other Processes in Continuous Time.- 17.1 Processes in continuous time.- 17.2 A few computations for the Poisson process.- 17.3 The Brownian motion process.- 17.4 A few computations for Brownian motion.- 17.5 Brownian motion as a limit of random walks.- 17.6 Exercises for Chapter 17.- Answers to Exercises.
£44.99
Springer Understanding Nonlinear Dynamics
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£44.99
Springer Probability Stochastic Processes and Queueing Theory The Mathematics of Computer Performance Modeling
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£85.49
Springer Rasch Models Foundations Recent Developments and Applications
Book SynopsisI: The Dichotomous Rasch Model.- 1. Some Background for Item Response Theory and the Rasch Model.- 2. Derivations of the Rasch Model.- 3. Estimation of Item Parameters.- 4. On Person Parameter Estimation in the Dichotomous Rasch Model.- 5. Testing the Rasch Model.- 6. The Assessment of Person Fit.- 7. Test Construction from Item Banks.- II: Extensions of the Dichotomous Rasch Model.- 8. The Linear Logistic Test Model.- 9. Linear Logistic Models for Change.- 10. Dynamic Generalizations of the Rasch Model.- 11. Linear and Repeated Measures Models for the Person Parameters.- 12. The One Parameter Logistic Model.- 13. Linear Logistic Latent Class Analysis and the Rasch Model.- 14. Mixture Distribution Rasch Models.- III: Polytomous Rasch Models and their Extensions.- 15. Polytomous Rasch Models and their Estimation.- 16. The Derivation of Polytomous Rasch Models.- 17. The Polytomous Rasch Model within the Class of Generalized Linear Symmetry Models.- 18. Tests of Fit for Polytomous Rasch MTable of ContentsI: The Dichotomous Rasch Model.- 1. Some Background for Item Response Theory and the Rasch Model.- 2. Derivations of the Rasch Model.- 3. Estimation of Item Parameters.- 4. On Person Parameter Estimation in the Dichotomous Rasch Model.- 5. Testing the Rasch Model.- 6. The Assessment of Person Fit.- 7. Test Construction from Item Banks.- II: Extensions of the Dichotomous Rasch Model.- 8. The Linear Logistic Test Model.- 9. Linear Logistic Models for Change.- 10. Dynamic Generalizations of the Rasch Model.- 11. Linear and Repeated Measures Models for the Person Parameters.- 12. The One Parameter Logistic Model.- 13. Linear Logistic Latent Class Analysis and the Rasch Model.- 14. Mixture Distribution Rasch Models.- III: Polytomous Rasch Models and their Extensions.- 15. Polytomous Rasch Models and their Estimation.- 16. The Derivation of Polytomous Rasch Models.- 17. The Polytomous Rasch Model within the Class of Generalized Linear Symmetry Models.- 18. Tests of Fit for Polytomous Rasch Models.- 19. Extended Rating Scale and Partial Credit Models for Assessing Change.- 20. Polytomous Mixed Rasch Models.- In Retrospect.- 21. What Georg Rasch Would Have Thought about this Book.- References.- Author Index.- Abbreviations.
£151.99
Springer New York Theory of Statistics Springer Series in Statistics
Book SynopsisThe aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D.Trade ReviewFrom the reviews: "Another excellent book in theory of statistics is by Mark J. Schervish. … Readers will enjoy reading this book to see how differently the theory can be presented … . This well written book contains nine chapters and four appendices. ... Each chapter has both easy and challenging problems. The book is suitable for graduate level statistical theory courses. Examples and illustrations are well explained. I liked the author’s presentation, and learned a lot from the book. I highly recommend this book to theoretical statisticians." (Ramalingam Shanmugam, Journal of Statistical Computation and Simulation, Vol. 74 (11), November, 2004)Table of ContentsContent.- 1: Probability Models.- 1.1 Background.- 1.1.1 General Concepts.- 1.1.2 Classical Statistics.- 1.1.3 Bayesian Statistics.- 1.2 Exchangeability.- 1.2.1 Distributional Symmetry.- 1.2.2 Frequency arid Exchangeability.- 1.3 Parametric Models.- 1.3.1 Prior, Posterior, and Predictive Distributions.- 1.3.2 Improper Prior Distributions.- 1.3.3 Choosing Probability Distributions.- 1.4 DeFinetti’s Representation Theorem.- 1.4.1 Understanding the Theorems.- 1.4.2 The Mathematical Statements.- 1.4.3 Some Examples.- 1.5 Proofs of DeFinetti’s Theorem and Related Results*.- 1.5.1 Strong Law of Large Numbers.- 1.5.2 The Bernoulli Case.- 1.5.3 The General Finite Case*.- 1.5.4 The General Infinite Case.- 1.5.5 Formal Introduction to Parametric Models*.- 1.6 Infinite-Dimensional Parameters*.- 1.6.1 Dirichlet Processes.- 1.6.2 Tailfree Processes+.- 1.7 Problems.- 2: Sufficient Statistics.- 2.1 Definitions.- 2.1.1 Notational Overview.- 2.1.2 Sufficiency.- 2.1.3 Minimal and Complete Sufficiency.- 2.1.4 Ancillarity.- 2.2 Exponential Families of Distributions.- 2.2.1 Basic Properties.- 2.2.2 Smoothness Properties.- 2.2.3 A Characterization Theorem*.- 2.3 Information.- 2.3.1 Fisher Information.- 2.3.2 Kullback-Leibler Information.- 2.3.3 Conditional Information*.- 2.3.4 Jeffreys’ Prior*.- 2.4 Extremal Families*.- 2.4.1 The Main Results.- 2.4.2 Examples.- 2.4.3 Proofs+.- 2.5 Problems.- Chapte 3: Decision Theory.- 3.1 Decision Problems.- 3.1.1 Framework.- 3.1.2 Elements of Bayesian Decision Theory.- 3.1.3 Elements of Classical Decision Theory.- 3.1.4 Summary.- 3.2 Classical Decision Theory.- 3.2.1 The Role of Sufficient Statistics.- 3.2.2 Admissibility.- 3.2.3 James—Stein Estimators.- 3.2.4 Minimax Rules.- 3.2.5 Complete Classes.- 3.3 Axiomatic Derivation of Decision Theory*.- 3.3.1 Definitions and Axioms.- 3.2.2 Examples.- 3.3.3 The Main Theorems.- 3.3.4 Relation to Decision Theory.- 3.3.5 Proofs of the Main Theorems*.- 3.3.6 State-Dependent Utility*.- 3.4 Problems.- 4: Hypothesis Testing.- 4.1 Introduction.- 4.1.1 A Special Kind of Decision Problem.- 4.1.2 Pure Significance Tests.- 4.2 Bayesian Solutions.- 4.2.1 Testing in General.- 4.2.2 Bayes Factors.- 4.3 Most Powerful Tests.- 4.3.1 Simple Hypotheses and Alternatives.- 4.3.2 Simple Hypotheses, Composite Alternatives.- 4.3.3 One-Sided Tests.- 4.3.4 Two-Sided Hypotheses.- 4.4 Unbiased Tests.- 4.4.1 General Results.- 4.4.2 Interval Hypotheses.- 4.4.3 Point Hypotheses.- 4.5 Nuisance Parameters.- 4.5.1 Neyinan Structure.- 4.5.2 Tests about Natural Parameters.- 4.5.3 Linear Combinations of Natural Parameters.- 4.5.4 Other Two-Sided Cases*.- 4.5.5 Likelihood Ratio Tests.- 4.5.6 The Standard F-Test as a Bayes Rule.- 4.6 P-Values.- 4.6.1 Definitions and Examples.- 4.6.2 P-Values and Bayes Factors.- 4.7 Problems.- 5: Estimation.- 5.1 Point Estimation.- 5.1.1 Minimum Variance Unbiased Estimation.- 5.1.2 Lower Bounds on the Variance of Unbiased Estimators.- 5.1.3 Maximum Likelihood Estimation.- 5.1.4 Bayesian Estimation.- 5.1.5 Robust Estimation*.- 5.2 Set Estimation.- 5.2.1 Confidence Sets.- 5.2.2 Prediction Sets*.- 5.2.3 Tolerance Sets*.- 5.2.4 Bayesian Set Estimation.- 5.2.5 Decision Theoretic Set Estimation.- 5.3 The Bootstrap*.- 5.3.1 The General Concept.- 5.3.2 Standard Deviations and Bias.- 5.3.3 Bootstrap Confidence Intervals.- 5.4 Problems.- 6: Equivariance*.- 6.1 Common Examples.- 6.1.1 Location Problems.- 6.1.2 Scale Problems.- 6.2 Equivariant Decision Theory.- 6.2.1 Groups of Transformations.- 6.2.2 Equivariance and Changes of Units.- 6.2.3 Minimum Risk Equivariant Decisions.- 6.3 Testing and Confidence Intervals*.- 6.3.1 P-Values in Invariant Problems.- 6.3.2 Equivariant Confidence Sets.- 6.3.3 Invariant Tests*.- 6.4 Problems.- 7: Large Sample Theory.- 7.1 Convergence Concepts.- 7.1.1 Deterministic Convergence.- 7.1.2 Stochastic Convergence.- 7.1.3 The Delta Method.- 7.2 Sample Quantiles.- 7.2.1 A Single Quantile.- 7.2.2 Several Quantiles.- 7.2.3 Linear Combinations of Quantiles*.- 7.3 Large Sample Estimation.- 7.3.1 Some Principles of Large Sample Estimation.- 7.3.2 Maximum Likelihood Estimators.- 7.3.3 MLEs in Exponential Families.- 7.3.4 Examples of Inconsistent MLEs.- 7.3.5 Asymptotic Normality of MLEs.- 7.3.6 Asymptotic Properties of M-Estimators.- 7.4 Large Sample Properties of Posterior Distributions.- 7.4.1 Consistency of Posterior Distributions+.- 7.4.2 Asymptotic Normality of Posterior Distributions.- 7.4.3 Laplace Approximations to Posterior Distributions*.- 7.4.4 Asymptotic Agreement of Predictive Distributions+.- 7.5 Large Sample Tests.- 7.5.1 Likelihood Ratio Tests.- 7.5.2 Chi-Squarcd Goodness of Fit Tests.- 7.6 Problems.- 8: Hierarchical Models.- 8.1 Introduction.- 8.1.1 General Hierarchical Models.- 8.1.2 Partial Exchangeability*.- 8.1.3 Examples of the Representation Theorem*.- 8.2 Normal Linear Models.- 8.2.1 One-Way ANOVA.- 8.2.2 Two-Way Mixed Model ANOVA*.- 8.2.3 Hypothesis Testing.- 8.3 Nonnormal Models*.- 8.3.1 Poisson Process Data.- 8.3.2 Bernoulli Process Data.- 8.4 Empirical Bayes Analysis*.- 8.4.1 Naïve Empirical Bayes.- 8.4.2 Adjusted Empirical Bayes.- 8.4.3 Unequal Variance Case.- 8.5 Successive Substitution Sampling.- 8.5.1 The General Algorithm.- 8.5.2 Normal Hierarchical Models.- 8.5.3 Nonnormal Models.- 8.6 Mixtures of Models.- 8.6.1 General Mixture Models.- 8.6.2 Outliers.- 8.6.3 Bayesian Robustness.- 8.7 Problems.- 9: Sequential Analysis.- 9.1 Sequential Decision Problems.- 9.2 The Sequential Probability Ratio Test.- 9.3 Interval Estimation*.- 9.4 The Relevancc of Stopping Rules.- 9.5 Problems.- Appendix A: Measure and Integration Theory.- A.1 Overview.- A.1.1 Definitions.- A.1.2 Measurable Functions.- A.1.3 Integration.- A.1.4 Absolute Continuity.- A.2 Measures.- A.3 Measurable Functions.- A.4 Integration.- A.5 Product Spaces.- A.6 Absolute Continuity.- A.7 Problems.- Appendix B: Probability Theory.- B.1 Overview.- B.1.1 Mathematical Probability.- B.1.2 Conditioning.- B.1.3 Limit Theorems.- B.2 Mathematical Probability.- B.2.1 Random Quantities and Distributions.- B.2.2 Some Useful Inequalities.- B.3 Conditioning.- B.3.1 Conditional Expectations.- B.3.2 Borel Spaces*.- B.3.3 Conditional Densities.- B.3.4 Conditional Independence.- B.3.5 The Law of Total Probability.- B.4 Limit Theorems.- B.4.1 Convergence in Distribution and in Probability.- B.4.2 Characteristic Functions.- B.5 Stochastic Processes.- B.5.1 Introduction.- B.5.3 Markov Chains*.- B.5.4 General Stochastic Processes.- B.6 Subjective Probability.- B.7 Simulation*.- B.8 Problems.- Appendix C: Mathematical Theorems Not Proven Here.- C.1 Real Analysis.- C.2 Complex Analysis.- C.3 Functional Analysis.- Appendix D: Summary of Distributions.- D.1 Univariate Continuous Distributions.- D.2 Univariate Discrete Distributions.- D.3 Multivariate Distributions.- References.- Notation and Abbreviation Index.- Name Index.
£104.49
Springer The State and the Labor Market Springer Studies in Work and Industry
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£85.49
Springer Applied Wavelet Analysis with SPLUS
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£85.49
Springer The SPSS Guide to the New Statistical Analysis of Data by TW Anderson and Jeremy D Finn Springer Lab Manuals
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Springer An Introduction to Measure and Probability Textbooks in Mathematical Sciences
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£64.99
Springer Breakthroughs in Statistics
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£74.93
Springer New York Linear Mixed Models for Longitudinal Data Springer Series in Statistics
Book SynopsisExamples.- A Model for Longitudinal Data.- Exploratory Data Analysis.- Estimation of the Marginal Model.- Inference for the Marginal Model.- Inference for the Random Effects.- Fitting Linear Mixed Models with SAS.- General Guidelines for Model Building.- Exploring Serial Correlation.- Local Influence for the Linear Mixed Model.- The Heterogeneity Model.- Conditional Linear Mixed Models.- Exploring Incomplete Data.- Joint Modeling of Measurements and Missingness.- Simple Missing Data Methods.- Selection Models.- Pattern-Mixture Models.- Sensitivity Analysis for Selection Models.- Sensitivity Analysis for Pattern-Mixture Models.- How Ignorable Is Missing At Random ?.- The Expectation-Maximization Algorithm.- Design Considerations.- Case Studies.Trade ReviewFrom the reviews: MATHEMATICAL REVIEWS "This book emphasizes practice rather than mathematical rigor and the majority of the chapters are explanatory rather than research oriented. In this respect, guidance and advice on practical issues are the main focus of the text. Hence it will be of interest to applied statisticians and biomedical researchers in industry, particularly in the pharmaceutical industry, medical public health organizations, contract research organizations, and academia." "This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Over 125 illustrations are included in the book. … I do believe that the book may serve as a useful reference to a broader audience. Since practical examples are provided as well as discussion of the leading software utilization, it may also be appropriate as a textbook in an advanced undergraduate-level or a graduate-level course in an applied statistics program." (Ana Ivelisse Avil és, Technometrics, Vol. 43 (3), 2001) "A practical book with a great many examples, including worked computer code and access to the datasets. … The authors state that the book covers ‘linear mixed models for continuous outcomes’ … . The book has four main strengths: its practical bent, its emphasis on exploratory analysis, its description of tools for model checking, and its treatment of dropout and missingness … . my impression of the book was … positive. Its strong practical nature and emphasis on dropout modelling are particularly welcome … ." (Harry Southworth, ISCB Newsletter, June, 2002) "This book is devoted to linear mixed-effects models with strong emphasis on the SAS procedure. Guidance and advice on practical issues are the main focus of the text. … It is of value to applied statisticians and biomedical researchers. … I recommend this book as a reference to applied statisticians and biomedical researchers, particularly in the pharmaceutical industry, medical and public organizations." (Wang Songgui, Zentralblatt MATH, Vol. 956, 2001)Table of ContentsIntroduction * Examples * A model for Longitudinal Data * Exploratory Data Analysis * Estimation of the Marginal Model * Inference for the Marginal Model * Inference for the Random Effects * Fitting Linear Mixed Models with SAS * General Guidelines for Model Building * Exploring Serial Correlation * Local Influence for the Linear Mixed Model * The Heterogeneity Model * Conditional Linear Mixed Models * Exploring Incomplete Data * Joint Modeling of Measurements and Missingness * Simple Missing Data Methods * Selection Models * Pattern-Mixture Models * Sensitivity Analysis for Selection Models * Sensitivity Analysis for Models * How Ignorable is Missing at Random? * The Expectation-Maximization Algorithm * Design Considerations * Case Studies
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Springer Counting The Art of Enumerative Combinatorics
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Springer Applied Functional Data Analysis Methods and Case Studies Springer Series in Statistics
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Springer-Verlag New York Inc. Elementary Probability Theory
Book Synopsis1 Set.- 1.1 Sample sets.- 1.2 Operations with sets.- 1.3 Various relations.- 1.4 Indicator.- Exercises.- 2 Probability.- 2.1 Examples of probability.- 2.2 Definition and illustrations.- 2.3 Deductions from the axioms.- 2.4 Independent events.- 2.5 Arithmetical density.- Exercises.- 3 Counting.- 3.1 Fundamental rule.- 3.2 Diverse ways of sampling.- 3.3 Allocation models; binomial coefficients.- 3.4 How to solve it.- Exercises.- 4 Random Variables.- 4.1 What is a random variable?.- 4.2 How do random variables come about?.- 4.3 Distribution and expectation.- 4.4 Integer-valued random variables.- 4.5 Random variables with densities.- 4.6 General case.- Exercises.- Appendix 1: Borel Fields and General Random Variables.- 5 Conditioning and Independence.- 5.1 Examples of conditioning.- 5.2 Basic formulas.- 5.3 Sequential sampling.- 5.4 Pólya's urn scheme.- 5.5 Independence and relevance.- 5.6 Genetical models.- Exercises.- 6 Mean, Variance, and Transforms.- 6.1 Basic properties of expectationTrade Review"In spite of the original edition of the book being nearly thirty years old, the text still has its role to play in first and second year undergraduate probability courses. It provides an excellent foundation to more advanced courses in the subject."Short Book Reviews, Vol. 23/3, Dec. 2003 "This edition is the third revision of a text on mathematical probability first published in 1974. The text is aimed at undergraduate mathematics students and is accessible to a general audience. The prose is accurate, entertaining, and dense with historical tidbits. Two concluding chapters on mathematical finance have been added to the eight chapters in the third edition by the second author." The American Statistician, May 2004 From the reviews of the fourth edition: "The main novelty in the fourth edition of this well-written book is the addition of new chapters … . The new chapters share the friendly yet rigorous style of the former ones. They begin with an account of the financial vocabulary, which is then expounded in probabilistic terms. … Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." (Ricardo Maronna, Statistical Papers, Vol. 45 (4), 2004)Table of ContentsSet * Probability * Counting * Random Variables * Conditioning and Independence * Mean, Variance and Transforms * Poisson and Normal Distributions * From Random Walks to Markov Chains * Mean-Variance Pricing Model * Option Pricing Theory
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Springer An Introduction to Probabilistic Modeling
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Springer SSpatialStats Users Manual for Windows and Unix Modern Acoustics and Signal
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Springer Discrete Probability
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Springer International Energy Economics 10 International Studies in Economic Modelling
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Springer Tools of Total Quality Introduction to Statistical Process Control An introduction to statistical process control
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Springer Designing for Quality An Introduction to the Best of Taguchi and Western Methods of Statistical Experimental Design
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