Format:
Online-Ressource (XIII, 307p, digital)
ISBN:
9780387687650
,
1280390875
,
9781280390876
Series Statement:
Use R 0
Content:
Introductory Examples: Simulation, Estimation, and Graphics -- Generating Random Numbers -- Monte Carlo Integration and Limit Theorems -- Sampling from Applied Probability Models -- Screening Tests -- Markov Chains with Two States -- Examples of Markov Chains with Larger State Spaces -- to Bayesian Estimation -- Using Gibbs Samplers to Compute Bayesian Posterior Distributions -- Using WinBUGS for Bayesian Estimation -- Appendix: Getting Started with R.
Content:
The first seven chapters use R for probability simulation and computation, including random number generation, numerical and Monte Carlo integration, and finding limiting distributions of Markov Chains with both discrete and continuous states. Applications include coverage probabilities of binomial confidence intervals, estimation of disease prevalence from screening tests, parallel redundancy for improved reliability of systems, and various kinds of genetic modeling. These initial chapters can be used for a non-Bayesian course in the simulation of applied probability models and Markov Chains. Chapters 8 through 10 give a brief introduction to Bayesian estimation and illustrate the use of Gibbs samplers to find posterior distributions and interval estimates, including some examples in which traditional methods do not give satisfactory results. WinBUGS software is introduced with a detailed explanation of its interface and examples of its use for Gibbs sampling for Bayesian estimation. No previous experience using R is required. An appendix introduces R, and complete R code is included for almost all computational examples and problems (along with comments and explanations). Noteworthy features of the book are its intuitive approach, presenting ideas with examples from biostatistics, reliability, and other fields; its large number of figures; and its extraordinarily large number of problems (about a third of the pages), ranging from simple drill to presentation of additional topics. Hints and answers are provided for many of the problems. These features make the book ideal for students of statistics at the senior undergraduate and at the beginning graduate levels. Eric A. Suess is Chair and Professor of Statistics and Biostatistics and Bruce E. Trumbo is Professor Emeritus of Statistics and Mathematics, both at California State University, East Bay. Professor Suess is experienced in applications of Bayesian methods and Gibbs sampling to epidemiology. Professor Trumbo is a fellow of the American Statistical Association and the Institute of Mathematical Statistics, and he is a recipient of the ASA Founders Award and the IMS Carver Medallion.
Note:
Includes bibliographical references (p. 301-304) and index
,
""Introduction to Probability Simulation and Gibbs Sampling Cardiology""; ""Preface""; ""Contents""; ""1 Introductory Examples: Simulation, Estimation, and Graphics""; ""1.1 Simulating Random Samples from Finite Populations""; ""1.2 Coverage Probabilities of Binomial Confidence Intervals""; ""1.3 Problems""; ""2 Generating Random Numbers""; ""2.1 Introductory Comments on Random Numbers""; ""2.2 Linear Congruential Generators""; ""2.3 Validating Desirable Properties of a Generator""; ""2.4 Transformations of Uniform Random Variables""; ""2.5 Transformations Involving Normal Random Variables""
,
""2.6 Problems""""3 Monte Carlo Integration and Limit Theorems""; ""3.1 Computing Probabilities of Intervals""; ""3.2 Convergence�The Law of Large Numbers""; ""3.3 Central Limit Theorem""; ""3.4 A Closer Look at Monte Carlo Integration""; ""3.5 When Is Simulation Appropriate?""; ""3.6 Problems""; ""4 Sampling from Applied Probability Models""; ""4.1 Models Based on Exponential Distributions""; ""4.2 Range of a Normal Sample""; ""4.3 Joint Distribution of the Sample Mean and Standard Deviation""; ""4.4 Nonparametric Bootstrap Distributions""; ""4.5 Problems""; ""5 Screening Tests""
,
""5.1 Prevalence, Sensitivity, and Specificity""""5.2 An Attempt to Estimate Prevalence""; ""5.3 Predictive Values""; ""5.4 Bayes' Theorem for Events""; ""5.5 Problems""; ""6 Markov Chains with Two States""; ""6.1 The Markov Property""; ""6.2 Transition Matrices""; ""6.3 Limiting Behavior of a 2-State Chain""; ""6.4 A Simple Gibbs Sampler""; ""6.5 Problems""; ""7 Examples of Markov Chains with Larger State Spaces""; ""7.1 Properties of K-State Chains""; ""7.2 Computing Long-Run Distributions""; ""7.3 Countably In¯nite State Spaces""; ""7.4 Continuous State Spaces""
,
""7.5 Uses of Markov Chains in Computation""""7.6 Problems""; ""8 Introduction to Bayesian Estimation""; ""8.1 Prior Distributions""; ""8.2 Data and Posterior Distributions""; ""8.3 Problems""; ""9 Using Gibbs Samplers to Compute Bayesian Posterior Distributions""; ""9.1 Bayesian Estimates of Disease Prevalence""; ""9.2 Bayesian Estimates of Normal Mean and Variance""; ""9.3 Bayesian Estimates of Components of Variance""; ""9.4 Problems""; ""10 Using WinBUGS for Bayesian Estimation""; ""10.1 What Is BUGS?""; ""10.2 Running WinBUGS: The Binomial Proportion""
,
""10.3 Running WinBUGS with a Script: Two-Sample Problem""""10.4 Running WinBUGS and MCMC Diagnostics: Variance Components""; ""10.5 A Final WinBUGS Example: Linear Regression""; ""10.6 Further Uses of WinBUGS""; ""10.7 Problems""; ""11 Appendix: Getting Started with R""; ""11.1 Basics""; ""11.1.1 Installation""; ""11.1.2 Using R as a Calculator""; ""11.1.3 Defining a Vector""; ""11.2 Using Vectors""; ""11.2.1 Simple Arithmetic with Vectors""; ""11.2.2 Indexes and Assignments""; ""11.2.3 Vector Functions""; ""11.2.4 Comparisons of Vectors""; ""11.3 Exploring Infinite Sequences""
,
""11.4 Loops""
Additional Edition:
ISBN 9780387402734
Additional Edition:
Erscheint auch als Druck-Ausgabe Suess, Eric A. Introduction to probability simulation and Gibbs sampling with R New York, NY : Springer, 2010 ISBN 9780387402734
Additional Edition:
ISBN 038740273X
Additional Edition:
Erscheint auch als Online-Ausgabe Suess, Eric A. Introduction to probability simulation and Gibbs sampling with R New York, NY : Springer, 2010 ISBN 9780387402734
Additional Edition:
ISBN 038740273X
Language:
English
Subjects:
Mathematics
Keywords:
Zufallszahlen
;
Gibbs-sampling
;
Simulation
;
Wahrscheinlichkeitstheorie
;
Stichprobe
;
Wahrscheinlichkeitsverteilung
DOI:
10.1007/978-0-387-68765-0
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
