Stochastics Books

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

Book SynopsisStructured in two parts, the first section focuses on probabilistic graphical models, while the second part deals with decision graphs, and in addition to the frameworks described in the previous edition, it also introduces Markov decision process and partially ordered decision problems.Trade ReviewFrom the reviews:MATHEMATICAL REVIEWS"This is indeed an invaluable text for students in information technology, engineering, and statistics. It is also very helpful for researchers in these fields and for those working in industry. The book is self-contained…The book has enough illustrative examples and exercises for the reader. All the illustrations are motivated by real applications. Moreover, the book provides a good balance between pure mathematical treatment and the applied aspects of the subject.""The Bayesian network (BN), or probabilistic expert system, is technology for automating human-life reasoning under uncertainty in specific contexts. … the book does an admirable job of concisely explaining a great range of concepts and techniques. … the book is very well written and to my knowledge nothing else meets its specific goal of quickly equipping the reader with both practical skills and sufficient theoretical background. … I certainly would not want to try to implement a BN application without reading this book.” (David Tritchler, Sankhya: Indian Journal of Statistics, Vol. 64 (B Part 3), 2002)"Professor Jensen is certainly one of the most influential researchers in the field of Bayesian networks and it is not surprising that this book represents a very clear and useful presentation of the main properties and use of graphical models. … I think that the present volume represents a useful integration of other material and a compact guide for either a student who wants an introduction to the field or a teacher who needs a reference for a course on probabilistic reasoning in AI." (Luigi Portinale, The Computer Journal, Vol. 46 (3), 2003)"This book is an introduction to Bayesian networks at an accessible level for first-year graduate or advanced undergraduate students. … I found this book to be an excellent introduction to the topic. It is well written, provides broad topic coverage, and is quite accessible to the non-expert. … I think Bayesian Networks and Decision Graphs would make a fine text for an introductory class in Bayesian networks or a useful reference for anyone interested in learning about the field." (David J. Marchette, Technometrics, Vol. 45 (2), 2003)"I can comfortably recommend this book as a primary source for topics related to Bayesian networks and decision graphs. This would be an excellent edition to any personal library." (Technometrics, Feburary 2008)From the reviews of the second edition:"The present book provides a very readable but also rigorous and comprehensive introduction to the subject. It would make a very good text for a graduate or an advanced undergraduate course. … Altogether, this is a very useful book for anyone interested in learning Bayesian networks without tears." (Jayanta K. Ghosh, International Statistical Reviews, Vol. 76 (2), 2008)"This book is the second edition of Jensen’s Bayesian Networks and Decision Graphs … . Each chapter ends with a summary section, bibliographic notes, and exercises. … provides a readable, self-contained, and above all, practical introduction to Bayesian networks and decision graphs. Its treatment is appropriate not just for statisticians, but also for computer scientists, engineers, and others researchers with appropriate mathematical background. … highly recommend it as a text or a useful reference for anyone interested in probabilistic graphical models or decision graphs." (Alyson G. Wilson, Journal of the American Statistical Association, Vol. 104 (485), March, 2009)“Devoted to Bayesian Networks or Graphical Models and Influence Diagrams, covering a full course with nice exercises … . It is useful as a reference for special topics. … strongly recommended for readers or user of BNs who are interested in specifying dependency models. … great importance to practitioners who try to find causality behind call-backs of products or crashes. … the book can be recommended to anybody working on the interface of operations research, AI, statistics and computer science.”­­­ (Hans-J. Lenz, Statistical Papers, Vol. 52, 2011)Table of ContentsCausal and Bayesian Networks * Part I: A Practical Guide to Normative Systems: Building Models * Learning, Adaptation, and Tuning * Decision Graphs * Part II: Algorithms for Normative Systems: Belief Updating in Bayesian Networks * Bayesian Network Analysis Tools * Algorithms for Influence Diagrams

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

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.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

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.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

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.

Read more less

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.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

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

Read more less

Book SynopsisA comprehensive introduction to a wide variety of statistical methods for the analysis of repeated measurements. It is designed to be both a useful reference for practitioners and a textbook for a graduate-level course focused on methods for the analysis of repeated measurements.Trade ReviewFrom the reviews: MATHEMATICAL REVIEWS "…the book covers a wide range of topics, including inference based on normal theory, repeated categorical outcomes and missing values. The book is based on lecture notes used by the author since 1991. Hence, the material and the structure of the book have been well tested by different audiences. Another feature of the book is the inclusion of a very rich collection of problems with excellent real data. Thus, it is a nice textbook for a semester course on repeated measurements and longitudinal data." SHORT BOOK REVIEW "Each major topic is introduced logically; background theory is clearly elucidated, and at least one example is carefully worked in detail. The use of eighty real sets of data, given in full, is a most attractive feature. Attention is concentrated on those techniques that are most readily available in software. ... This should prove to be a very useful text for teacher, student and practitioner alike." JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION "Most other books on repeated measurements tend to focus on specialized topics. In my opinion, [this] book is the most comprehensive and readable of the lot. I would highly recommend its use as a text for a semester-length graduate course for biostatistics and statistics students and also as resource book for consulting biostatisticians and statisticians. In addition, this book would be a valuable resource for students from other fields of study (e.g., the health sciences) who have a statistical aptitude. The book is definitely worth the price." "The intention of the book is ‘to provide a reasonably comprehensive overview of methods for the analysis of repeated measurements’ with focus on standard statistical methods … . In my opinion the book gives a nice, comprehensive overview of methods for the analysis of repeated measurements. … The availability of data sets, overheads, etc. is a very valuable supplement for both teachers and students. … The book … could be a natural choice for a course in repeated measurements for graduate students in (bio-) statistics." (Niels Trolle Andersen, Statistics in Medicine, Vol. 24 (5), 2005) "This book is a very interesting and comprehensive summary of a wide selection of statistical methods for the analysis of repeated measurements. It is indeed an ideal and carefully written text to be used as a reference guide for practitioners and, in addition, as a great, up to date and very complete textbook for a graduate-level course in Statistics and/or Biostatistics. … I highly recommend Statistical Methods … as a good reference book for anyone interested in looking into the different available methodologies … ." (Vicente Núñez-Antón, Journal of Applied Statistics, Vol. 30 (10), December, 2003) "This book provides a comprehensive introduction to a wide variety of statistical methods for the analysis of repeated measurements. … In conclusion, as a course text on repeated measurements this book clearly has major strengths over others in that it provides coverage on a wide range of topics and provides extensive further reading material. … I would recommend this text as a general reference book on repeated measurements which would make a worthwhile addition to a departmental library." (Fiona Holland, Pharmaceutical Statistics, 2003) "Most other books on repeated measurements … tend to focus on specialized topics. In my opinion, Statistical Methods for the Analysis of Repeated Measurements book is the most comprehensive and readable of the lot. I would highly recommend its use as a text for a semester-length graduate course for biostatistics and statistics students and … for consulting biostatisticians and statisticians. … a valuable resource for students from other fields of study … who have a statistical aptitude. The book is definitely worth the price." (Melvin L. Moeschberger, Journal of the American Statistical Association, March, 2003) "The book aims at describing, discussing and demonstrating a variety of statistical methods for the analysis of repeated measurements … . the book covers a very wide range of topics, including inference based on normal theory, repeated categorical outcomes and missing values. … Another feature of the book is the inclusion of a very rich collection of problems with excellent real data. Thus, it is a nice textbook for a semester course on repeated measurements and longitudinal data." (Jack C. Lee, Mathematical Reviews, 2003 e) "This book is intended to provide a comprehensive introduction to a wide range of statistical methods for the analysis of repeated measurements. … For use in a course, I would use it for an applied graduate-level statistics course on linear models for analysis of repeated measurements. This text is useful not only with regards to the statistical methods, but also for the real data examples that can be explored with the various models and methods under study." (James R. Kenyon, Technometrics, Vol. 45 (1), 2003) "This book provides a reasonably comprehensive overview of a wide variety of statistical methods for the analysis of repeated measurements … . The important features of this book include a summary of both classical and recent methods for continuous and categorical outcome variables, numerous homework problems, and the extensive use of real data sets in examples. … This book will be of interest to graduate students in statistics and biostatistics as well as to practicing statisticians in academic, industry and research institutions.” (Ivan Krivý, Zentralblatt MATH, Vol. 985, 2002)Table of ContentsIntroduction * Univariate Methods * Normal-Theory Methods: Unstructured Multivariate Approach * Normal Theory Methods: Multivariate Analysis of Variance * Normal-Theory Methods: Repeated Measures ANOVA * Normal Theory Methods: Linear Mixed Models * Weighted Least Squares Analysis of Repeated Categorical Outcomes * Randomization Model Methods for One-Sample Repeated Measurements * Methods Based on Extensions of Generalized Linear Models * Nonparametric Methods

Read more less

Book SynopsisPoint processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology. This volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction.Trade ReviewFrom the reviews of the second edition: "This is an important treatise on the mathematical theory relevant to a wide variety of random processes…The reader will find excellent treatments of important advanced topics such as Cox, renewal, Wold, marked, cluster, and other specialized processes, plus concise but useful appendices on topology, measure theory, metric spaces, martingales, and the like." Technometrics, May 2004 "This revision splits the lengthy first version into two volumes now subtitled Volume I: Elementary Theory and Methods and Volume II: Models and General Theory and Structure...this first volume is well worth its price." Journal of the American Statistical Association, September 2004 "The theory of point processes has undergone an explosive expansion in the last two decades. There was a genuine need for a single source that would contain a survey of the general theory of Point Process accessible to beginning graduate students and researchers in the field but at the same time would include some of the more recent – though relatively advanced and technically difficult – developments in the area. The present edition of the book addresses that need quite successfully.” (Alok Goswami, Sankhya, Vol. 67 (1), 2005) "It is a pleasure to announce that a second edition of the classic book ‘An Introduction to the Theory of Point Processes’ has been published. … many chapters and sections were thoroughly reworked. This holds true in particular for the exercises, which are obviously produced with particular love. … The reviewer is sure that the owners of the first edition will buy also the second, and for many younger readers it will become the beloved key reference to point processes." (Dietrich Stoyan, Metrika, May, 2004) "The second edition of this monograph is divided into two volumes. The first one is concentrated on introductory material and models, the second one on structure and general theory. … suitable as a textbook with many exercises for beginners as well as a source for scientists interested in high level applications of point processes." (Uwe Küchler, Zentralblatt MATH, Vol. 1026, 2004) "The first edition of this book by two major research workers in the field speedily established itself as an authoritative account of an important and rapidly developing subject. In this substantially revised and expanded second edition, the authors have wisely decided to divide the book into two parts leaving some of the very technical material … to a second volume. … The book is likely to establish itself quickly as a major contribution to the field." (D. R. Cox, Short Book Reviews, Vol. 23 (2), 2003)Table of ContentsEarly History * Basic Properties of the Poisson Process * Simple Results for Stationary Point Processes on the Line * Renewal Processes * Finite Point Processes * Models Constructed via Conditioning: Cox, Cluster,and Marked Point Processes * Conditional Intensities and Likelihoods * Second Order Properties of Stationary Point Processes

Read more less

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

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

Book Synopsis1 Controlled Markov Processes.- 1.1 Introduction.- 1.2 Stochastic Control Problems.- 1.3 Examples.- 1.4 Further Comments.- 2 Discounted Reward Criterion.- 2.1 Introduction.- 2.2 Optimality Conditions.- 2.3 Asymptotic Discount Optimality.- 2.4 Approximation of MCM's.- 2.5 Adaptive Control Models.- 2.6 Nonparametric Adaptive Control.- 2.7 Comments and References.- 3 Average Reward Criterion.- 3.1 Introduction.- 3.2 The Optimality Equation.- 3.3 Ergodicity Conditions.- 3.4 Value Iteration.- 3.5 Approximating Models.- 3.6 Nonstationary Value Iteration.- 3.7 Adaptive Control Models.- 3.8 Comments and References.- 4 Partially Observable Control Models.- 4.1 Introduction.- 4.2 PO-CM: Case of Known Parameters.- 4.3 Transformation into a CO Control Problem.- 4.4 Optimal I-Policies.- 4.5 PO-CM's with Unknown Parameters.- 4.6 Comments and References.- 5 Parameter Estimation in MCM's.- 5.1 Introduction.- 5.2 Contrast Functions.- 5.3 Minimum Contrast Estimators.- 5.4 Comments and References.- 6 Discretization Procedures.- 6.1 Introduction.- 6.2 Preliminaries.- 6.3 The Non-Adaptive Case.- 6.4 Adaptive Control Problems.- 6.5 Proofs.- 6.6 Comments and References.- Appendix A. Contraction Operators.- Appendix B. Probability Measures.- Total Variation Norm.- Weak Convergence.- Appendix C. Stochastic Kernels.- Appendix D. Multifunctions and Measurable Selectors.- The Hausdorff Metric.- Multifunctions.- References.- Author Index.Table of Contents1 Controlled Markov Processes.- 1.1 Introduction.- 1.2 Stochastic Control Problems.- Control Models.- Policies.- Performance Criteria.- Control Problems.- 1.3 Examples.- An Inventory/Production System.- Control of Water Reservoirs.- Fisheries Management.- Nonstationary MCM’s.- Semi-Markov Control Models.- 1.4 Further Comments.- 2 Discounted Reward Criterion.- 2.1 Introduction.- Summary.- 2.2 Optimality Conditions.- Continuity of ?*.- 2.3 Asymptotic Discount Optimality.- 2.4 Approximation of MCM’s.- Nonstationary Value-Iteration.- Finite-State Approximations.- 2.5 Adaptive Control Models.- Preliminaries.- Nonstationary Value-Iteration.- The Principle of Estimation and Control.- Adaptive Policies.- 2.6 Nonparametric Adaptive Control.- The Parametric Approach.- New Setting.- The Empirical Distribution Process.- Nonparametric Adaptive Policies.- 2.7 Comments and References.- 3 Average Reward Criterion.- 3.1 Introduction.- Summary.- 3.2 The Optimality Equation.- 3.3 Ergodicity Conditions.- 3.4 Value Iteration.- Uniform Approximations.- Successive Averagings.- 3.5 Approximating Models.- 3.6 Nonstationary Value Iteration.- Nonstationary Successive Averagings.- Discounted-Like NVI.- 3.7 Adaptive Control Models.- Preliminaries.- The Principle of Estimation and Control (PEC).- Nonstationary Value Iteration (NVI).- 3.8 Comments and References.- 4 Partially Observable Control Models.- 4.1 Introduction.- Summary.- 4.2 PO-CM: Case of Known Parameters.- The PO Control Problem.- 4.3 Transformation into a CO Control Problem.- I-Policies.- The New Control Model.- 4.4 Optimal I-Policies.- 4.5 PO-CM’s with Unknown Parameters.- PEC and NVI I-Policies.- 4.6 Comments and References.- 5 Parameter Estimation in MCM’s.- 5.1 Introduction.- Summary.- 5.2 Contrast Functions.- 5.3 Minimum Contrast Estimators.- 5.4 Comments and References.- 6 Discretization Procedures.- 6.1 Introduction.- Summary.- 6.2 Preliminaries.- 6.3 The Non-Adaptive Case.- A Non-Recursive Procedure.- A Recursive Procedure.- 6.4 Adaptive Control Problems.- Preliminaries.- Discretization of the PEC Adaptive Policy.- Discretization of the NVI Adaptive Policy.- 6.5 Proofs.- The Non-Adaptive Case.- The Adaptive Case.- 6.6 Comments and References.- Appendix A. Contraction Operators.- Appendix B. Probability Measures.- Total Variation Norm.- Weak Convergence.- Appendix C. Stochastic Kernels.- Appendix D. Multifunctions and Measurable Selectors.- The Hausdorff Metric.- Multifunctions.- References.- Author Index.

Read more less

Book Synopsis1 Martingales, Stopping Times, and Filtrations.- 1.1. Stochastic Processes and ?-Fields.- 1.2. Stopping Times.- 1.3. Continuous-Time Martingales.- 1.4. The DoobMeyer Decomposition.- 1.5. Continuous, Square-Integrable Martingales.- 1.6. Solutions to Selected Problems.- 1.7. Notes.- 2 Brownian Motion.- 2.1. Introduction.- 2.2. First Construction of Brownian Motion.- 2.3. Second Construction of Brownian Motion.- 2.4. The SpaceC[0, ?), Weak Convergence, and Wiener Measure.- 2.5. The Markov Property.- 2.6. The Strong Markov Property and the Reflection Principle.- 2.7. Brownian Filtrations.- 2.8. Computations Based on Passage Times.- 2.9. The Brownian Sample Paths.- 2.10. Solutions to Selected Problems.- 2.11. Notes.- 3 Stochastic Integration.- 3.1. Introduction.- 3.2. Construction of the Stochastic Integral.- 3.3. The Change-of-Variable Formula.- 3.4. Representations of Continuous Martingales in Terms of Brownian Motion.- 3.5. The Girsanov Theorem.- 3.6. Local Time and a Generalized Itô Rule for Brownian Motion.- 3.7. Local Time for Continuous Semimartingales.- 3.8. Solutions to Selected Problems.- 3.9. Notes.- 4 Brownian Motion and Partial Differential Equations.- 4.1. Introduction.- 4.2. Harmonic Functions and the Dirichlet Problem.- 4.3. The One-Dimensional Heat Equation.- 4.4. The Formulas of Feynman and Kac.- 4.5. Solutions to selected problems.- 4.6. Notes.- 5 Stochastic Differential Equations.- 5.1. Introduction.- 5.2. Strong Solutions.- 5.3. Weak Solutions.- 5.4. The Martingale Problem of Stroock and Varadhan.- 5.5. A Study of the One-Dimensional Case.- 5.6. Linear Equations.- 5.7. Connections with Partial Differential Equations.- 5.8. Applications to Economics.- 5.9. Solutions to Selected Problems.- 5.10. Notes.- 6 P. Lévy's Theory of Brownian Local Time.-6.1. Introduction.- 6.2. Alternate Representations of Brownian Local Time.- 6.3. Two Independent Reflected Brownian Motions.- 6.4. Elastic Brownian Motion.- 6.5. An Application: Transition Probabilities of Brownian Motion with Two-Valued Drift.- 6.6. Solutions to Selected Problems.- 6.7. Notes.Trade ReviewSecond Edition I. Karatzas and S.E. Shreve Brownian Motion and Stochastic Calculus "A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."—MATHEMATICAL REVIEWSTable of Contents1 Martingales, Stopping Times, and Filtrations.- 1.1. Stochastic Processes and ?-Fields.- 1.2. Stopping Times.- 1.3. Continuous-Time Martingales.- A. Fundamental inequalities.- B. Convergence results.- C. The optional sampling theorem.- 1.4. The Doob—Meyer Decomposition.- 1.5. Continuous, Square-Integrable Martingales.- 1.6. Solutions to Selected Problems.- 1.7. Notes.- 2 Brownian Motion.- 2.1. Introduction.- 2.2. First Construction of Brownian Motion.- A. The consistency theorem.- B. The Kolmogorov—?entsov theorem.- 2.3. Second Construction of Brownian Motion.- 2.4. The SpaceC[0, ?), Weak Convergence, and Wiener Measure.- A. Weak convergence.- B. Tightness.- C. Convergence of finite-dimensional distributions.- D. The invariance principle and the Wiener measure.- 2.5. The Markov Property.- A. Brownian motion in several dimensions.- B. Markov processes and Markov families.- C. Equivalent formulations of the Markov property.- 2.6. The Strong Markov Property and the Reflection Principle.- A. The reflection principle.- B. Strong Markov processes and families.- C. The strong Markov property for Brownian motion.- 2.7. Brownian Filtrations.- A. Right-continuity of the augmented filtration for a strong Markov process.- B. A “universal” filtration.- C. The Blumenthal zero-one law.- 2.8. Computations Based on Passage Times.- A. Brownian motion and its running maximum.- B. Brownian motion on a half-line.- C. Brownian motion on a finite interval.- D. Distributions involving last exit times.- 2.9. The Brownian Sample Paths.- A. Elementary properties.- B. The zero set and the quadratic variation.- C. Local maxima and points of increase.- D. Nowhere differentiability.- E. Law of the iterated logarithm.- F. Modulus of continuity.- 2.10. Solutions to Selected Problems.- 2.11. Notes.- 3 Stochastic Integration.- 3.1. Introduction.- 3.2. Construction of the Stochastic Integral.- A. Simple processes and approximations.- B. Construction and elementary properties of the integral.- C. A characterization of the integral.- D. Integration with respect to continuous, local martingales.- 3.3. The Change-of-Variable Formula.- A. The Itô rule.- B. Martingale characterization of Brownian motion.- C. Bessel processes, questions of recurrence.- D. Martingale moment inequalities.- E. Supplementary exercises.- 3.4. Representations of Continuous Martingales in Terms of Brownian Motion.- A. Continuous local martingales as stochastic integrals with respect to Brownian motion.- B. Continuous local martingales as time-changed Brownian motions.- C. A theorem of F. B. Knight.- D. Brownian martingales as stochastic integrals.- E. Brownian functionals as stochastic integrals.- 3.5. The Girsanov Theorem.- A. The basic result.- B. Proof and ramifications.- C. Brownian motion with drift.- D. The Novikov condition.- 3.6. Local Time and a Generalized Itô Rule for Brownian Motion.- A. Definition of local time and the Tanaka formula.- B. The Trotter existence theorem.- C. Reflected Brownian motion and the Skorohod equation.- D. A generalized Itô rule for convex functions.- E. The Engelbert—Schmidt zero-one law.- 3.7. Local Time for Continuous Semimartingales.- 3.8. Solutions to Selected Problems.- 3.9. Notes.- 4 Brownian Motion and Partial Differential Equations.- 4.1. Introduction.- 4.2. Harmonic Functions and the Dirichlet Problem.- A. The mean-value property.- B. The Dirichlet problem.- C. Conditions for regularity.- D. Integral formulas of Poisson.- E. Supplementary exercises.- 4.3. The One-Dimensional Heat Equation.- A. The Tychonoff uniqueness theorem.- B. Nonnegative solutions of the heat equation.- C. Boundary crossing probabilities for Brownian motion.- D. Mixed initial/boundary value problems.- 4.4. The Formulas of Feynman and Kac.- A. The multidimensional formula.- B. The one-dimensional formula.- 4.5. Solutions to selected problems.- 4.6. Notes.- 5 Stochastic Differential Equations.- 5.1. Introduction.- 5.2. Strong Solutions.- A. Definitions.- B. The Itô theory.- C. Comparison results and other refinements.- D. Approximations of stochastic differential equations.- E. Supplementary exercises.- 5.3. Weak Solutions.- A. Two notions of uniqueness.- B. Weak solutions by means of the Girsanov theorem.- C. A digression on regular conditional probabilities.- D. Results of Yamada and Watanabe on weak and strong solutions.- 5.4. The Martingale Problem of Stroock and Varadhan.- A. Some fundamental martingales.- B. Weak solutions and martingale problems.- C. Well-posedness and the strong Markov property.- D. Questions of existence.- E. Questions of uniqueness.- F. Supplementary exercises.- 5.5. A Study of the One-Dimensional Case.- A. The method of time change.- B. The method of removal of drift.- C. Feller’s test for explosions.- D. Supplementary exercises.- 5.6. Linear Equations.- A. Gauss—Markov processes.- B. Brownian bridge.- C. The general, one-dimensional, linear equation.- D. Supplementary exercises.- 5.7. Connections with Partial Differential Equations.- A. The Dirichlet problem.- B. The Cauchy problem and a Feynman—Kac representation.- C. Supplementary exercises.- 5.8. Applications to Economics.- A. Portfolio and consumption processes.- B. Option pricing.- C. Optimal consumption and investment (general theory).- D. Optimal consumption and investment (constant coefficients).- 5.9. Solutions to Selected Problems.- 5.10. Notes.- 6 P. Lévy’s Theory of Brownian Local Time.- 6.1. Introduction.- 6.2. Alternate Representations of Brownian Local Time.- A. The process of passage times.- B. Poisson random measures.- C. Subordinators.- D. The process of passage times revisited.- E. The excursion and downcrossing representations of local time.- 6.3. Two Independent Reflected Brownian Motions.- A. The positive and negative parts of a Brownian motion.- B. The first formula of D. Williams.- C. The joint density of (W(t), L(t), ? +(t)).- 6.4. Elastic Brownian Motion.- A. The Feynman—Kac formulas for elastic Brownian motion.- B. The Ray—Knight description of local time.- C. The second formula of D. Williams.- 6.5. An Application: Transition Probabilities of Brownian Motion with Two-Valued Drift.- 6.6. Solutions to Selected Problems.- 6.7. Notes.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

Book SynopsisComputational inference is based on an approach to statistical methods that uses modern computational power to simulate distributional properties of estimators and test statistics.Trade ReviewFrom the reviews:“This is a book that covers many of the computational issues that statisticians will encounter as part of their research and applied work. … The writing in the book is quite clear and the author has done a good job providing the essence of each topic. … Overall, I think this is an excellent book. … This book will give a graduate student a good overview of the field. There are exercises provided for each chapter together with some solutions.” (Michael J. Evans, Mathematical Reviews, Issue 2011 b)“This book is a superior treatment of the important subject of statistical computing. I strongly recommend this book to anyone who analyzes data using either a commercial statistical software package or statistical computer programs written by the user or someone else. Thus this book is important not only for data oriented statisticians but for econometricians, psychometricians, political methodologists and biometricians as well. … All terms in this work including computing terms are clearly defined.” (Melvin Hinich, Technometrics, Vol. 53 (1), February, 2011)“I greatly appreciated the author’s command of both numerical and statistical computing … . The book also contains many exercises that substantiate the concepts, with solutions and hints in the appendix, an extensive bibliography, and a link to further literature and notes. The target readership includes undergraduates, postgraduates in statistics and allied fields such as computer science and mathematics, scientific research workers, and practitioners of statistics and numerical techniques. … I strongly recommend it for all scientific libraries.” (Soubhik Chakraborty, ACM Computing Reviews, October, 2010)“This book has a very large scope in that … it covers the dual fields of computational statistics and of statistical computing. … must-read for all students and researchers engaging into any kind of serious statistical programming. … is well-written, in a lively and personal style. … a reference book that should appear in the shortlist of any computational statistics/statistical computing graduate course as well as on the shelves of any researchers supporting his or her statistical practice with a significant dose of computing backup.”­­­ (Christian P. Robert, Statistical and Computation, Vol. 21, 2011)Table of ContentsPreliminaries.- Mathematical and Statistical Preliminaries.- Statistical Computing.- Computer Storage and Arithmetic.- Algorithms and Programming.- Approximation of Functions and Numerical Quadrature.- Numerical Linear Algebra.- Solution of Nonlinear Equations and Optimization.- Generation of Random Numbers.- Methods of Computational Statistics.- Graphical Methods in Computational Statistics.- Tools for Identification of Structure in Data.- Estimation of Functions.- Monte Carlo Methods for Statistical Inference.- Data Randomization, Partitioning, and Augmentation.- Bootstrap Methods.- Exploring Data Density and Relationships.- Estimation of Probability Density Functions Using Parametric Models.- Nonparametric Estimation of Probability Density Functions.- Statistical Learning and Data Mining.- Statistical Models of Dependencies.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

Book SynopsisIn the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case.Trade ReviewFrom the reviews: SIAM REVIEW "The presentation of this book is systematic and self-contained…Summing up, this book is a very good addition to the control literature, with original features not found in other reference books. Certain parts could be used as basic material for a graduate (or postgraduate) course…This book is highly recommended to anyone who wishes to study the relationship between Pontryagin’s maximum principle and Bellman’s dynamic programming principle applied to diffusion processes." MATHEMATICS REVIEW This is an authoratative book which should be of interest to researchers in stochastic control, mathematical finance, probability theory, and applied mathematics. Material out of this book could also be used in graduate courses on stochastic control and dynamic optimization in mathematics, engineering, and finance curricula. Tamer Basar, Math. ReviewTable of Contents1. Basic Stochastic Calculus.- 1. Probability.- 1.1. Probability spaces.- 1.2. Random variables.- 1.3. Conditional expectation.- 1.4. Convergence of probabilities.- 2. Stochastic Processes.- 2.1. General considerations.- 2.2. Brownian motions.- 3. Stopping Times.- 4. Martingales.- 5. Itô’s Integral.- 5.1. Nondifferentiability of Brownian motion.- 5.2. Definition of Itô’s integral and basic properties.- 5.3. Itô’s formula.- 5.4. Martingale representation theorems.- 6. Stochastic Differential Equations.- 6.1. Strong solutions.- 6.2. Weak solutions.- 6.3. Linear SDEs.- 6.4. Other types of SDEs.- 2. Stochastic Optimal Control Problems.- 1. Introduction.- 2. Deterministic Cases Revisited.- 3. Examples of Stochastic Control Problems.- 3.1. Production planning.- 3.2. Investment vs. consumption.- 3.3. Reinsurance and dividend management.- 3.4. Technology diffusion.- 3.5. Queueing systems in heavy traffic.- 4. Formulations of Stochastic Optimal Control Problems.- 4.1. Strong formulation.- 4.2. Weak formulation.- 5. Existence of Optimal Controls.- 5.1. A deterministic result.- 5.2. Existence under strong formulation.- 5.3. Existence under weak formulation.- 6. Reachable Sets of Stochastic Control Systems.- 6.1. Nonconvexity of the reachable sets.- 6.2. Noncloseness of the reachable sets.- 7. Other Stochastic Control Models.- 7.1. Random duration.- 7.2. Optimal stopping.- 7.3. Singular and impulse controls.- 7.4. Risk-sensitive controls.- 7.5. Ergodic controls.- 7.6. Partially observable systems.- 8. Historical Remarks.- 3. Maximum Principle and Stochastic Hamiltonian Systems.- 1. Introduction.- 2. The Deterministic Case Revisited.- 3. Statement of the Stochastic Maximum Principle.- 3.1. Adjoint equations.- 3.2. The maximum principle and stochastic Hamiltonian systems.- 3.3. A worked-out example.- 4. A Proof of the Maximum Principle.- 4.1. A moment estimate.- 4.2. Taylor expansions.- 4.3. Duality analysis and completion of the proof.- 5. Sufficient Conditions of Optimality.- 6. Problems with State Constraints.- 6.1. Formulation of the problem and the maximum principle.- 6.2. Some preliminary lemmas.- 6.3. A proof of Theorem 6.1.- 7. Historical Remarks.- 4. Dynamic Programming and HJB Equations.- 1. Introduction.- 2. The Deterministic Case Revisited.- 3. The Stochastic Principle of Optimality and the HJB Equation.- 3.1. A stochastic framework for dynamic programming.- 3.2. Principle of optimality.- 3.3. The HJB equation.- 4. Other Properties of the Value Function.- 4.1. Continuous dependence on parameters.- 4.2. Semiconcavity.- 5. Viscosity Solutions.- 5.1. Definitions.- 5.2. Some properties.- 6. Uniqueness of Viscosity Solutions.- 6.1. A uniqueness theorem.- 6.2. Proofs of Lemmas 6.6 and 6.7.- 7. Historical Remarks.- 5. The Relationship Between the Maximum Principle and Dynamic Programming.- 1. Introduction.- 2. Classical Hamilton-Jacobi Theory.- 3. Relationship for Deterministic Systems.- 3.1. Adjoint variable and value function: Smooth case.- 3.2. Economic interpretation.- 3.3. Methods of characteristics and the Feynman-Kac formula.- 3.4. Adjoint variable and value function: Nonsmooth case.- 3.5. Verification theorems.- 4. Relationship for Stochastic Systems.- 4.1. Smooth case.- 4.2. Nonsmooth case: Differentials in the spatial variable.- 4.3. Nonsmooth case: Differentials in the time variable.- 5. Stochastic Verification Theorems.- 5.1. Smooth case.- 5.2. Nonsmooth case.- 6. Optimal Feedback Controls.- 7. Historical Remarks.- 6. Linear Quadratic Optimal Control Problems.- 1. Introduction.- 2. The Deterministic LQ Problems Revisited.- 2.1. Formulation.- 2.2. A minimization problem of a quadratic functional.- 2.3. A linear Hamiltonian system.- 2.4. The Riccati equation and feedback optimal control.- 3. Formulation of Stochastic LQ Problems.- 3.1. Statement of the problems.- 3.2. Examples.- 4. Finiteness and Solvability.- 5. A Necessary Condition and a Hamiltonian System.- 6. Stochastic Riccati Equations.- 7. Global Solvability of Stochastic Riccati Equations.- 7.1. Existence: The standard case.- 7.2. Existence: The case C = 0, S = 0, and Q, G ?0.- 7.3. Existence: The one-dimensional case.- 8. A Mean-variance Portfolio Selection Problem.- 9. Historical Remarks.- 7. Backward Stochastic Differential Equations.- 1. Introduction.- 2. Linear Backward Stochastic Differential Equations.- 3. Nonlinear Backward Stochastic Differential Equations.- 3.1. BSDEs in finite deterministic durations: Method of contraction mapping.- 3.2. BSDEs in random durations: Method of continuation.- 4. Feynman—Kac-Type Formulae.- 4.1. Representation via SDEs.- 4.2. Representation via BSDEs.- 5. Forward—Backward Stochastic Differential Equations.- 5.1. General formulation and nonsolvability.- 5.2. The four-step scheme, a heuristic derivation.- 5.3. Several solvable classes of FBSDEs.- 6. Option Pricing Problems.- 6.1. European call options and the Black--Scholes formula.- 6.2. Other options.- 7. Historical Remarks.- References.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

Book SynopsisThe 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. [A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference. -American Scientist There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings. -Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference wTable of ContentsIntroduction. 1. Operator Semigroups. 2. Stochastic Processes and Martingales. 3. Convergence of Probability Measures. 4. Generators and Markov Processes. 5. Stochastic Integral Equations. 6. Random Time Changes. 7. Invariance Principles and Diffusion Approximations. 8. Examples of Generators. 9. Branching Processes. 10. Genetic Models. 11. Density Dependent Population Processes. 12. Random Evolutions. Appendixes. References. Index. Flowchart.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less