Understanding Computational Bayesian Statistics [NOOK Book]

Overview

Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common ...

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Understanding Computational Bayesian Statistics

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Overview

Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common statistical models, including the multiple linear regression model, the hierarchical mean model, the logistic regression model, and the proportional hazards model.

The book begins with an outline of the similarities and differences between Bayesian and the likelihood approaches to statistics. Subsequent chapters present key techniques for using computer software to draw Monte Carlo samples from the incompletely known posterior distribution and performing the Bayesian inference calculated from these samples. Topics of coverage include:

Direct ways to draw a random sample from the posterior by reshaping a random sample drawn from an easily sampled starting distribution

The distributions from the one-dimensional exponential family

Markov chains and their long-run behavior

The Metropolis-Hastings algorithm

Gibbs sampling algorithm and methods for speeding up convergence

Markov chain Monte Carlo sampling

Using numerous graphs and diagrams, the author emphasizes a step-by-step approach to computational Bayesian statistics. At each step, important aspects of application are detailed, such as how to choose a prior for logistic regression model, the Poisson regressionmodel, and the proportional hazards model. A related Web site houses R functions and Minand macros for Bayesian analysis and Monte Carlo simulations, and detailed appendices in the book guide readers through the use of these software packages.

Understanding Computational Bayesian Statistics is an excellent book for courses on computational statistics at the upper-level undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who use computer programs to conduct statistical analyses of data and solve problems in their everyday work.

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Editorial Reviews

From the Publisher
"Understanding computational Bayesian statistics is an excellent book for courses on computational statistics at the advanced undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who use computer programs to conduct statistical analyses of data and solve problems in their everyday work." (Mathematical Reviews, 2011)
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Product Details

  • ISBN-13: 9781118209929
  • Publisher: Wiley
  • Publication date: 9/20/2011
  • Series: Wiley Series in Computational Statistics , #644
  • Sold by: Barnes & Noble
  • Format: eBook
  • Edition number: 1
  • Pages: 336
  • File size: 12 MB
  • Note: This product may take a few minutes to download.

Meet the Author

William M. Bolstad, PhD, is Senior Lecturer in the Department of Statistics at The University of Waikato (New Zealand). Dr. Bolstad's research interests include Bayesian statistics, MCMC methods, recursive estimation techniques, multiprocess dynamic time series models, and forecasting. He is the author of Introduction to Bayesian Statistics, Second Edition, also published by Wiley.
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Read an Excerpt

catalogimages.wiley.com/images/db/pdf/9780470046098.excerpt.pdf
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Table of Contents

Preface
1 Introduction to statistical science 1
2 Scientific data gathering 13
3 Displaying and summarizing data 29
4 Logic, probability, and uncertainty 55
5 Discrete random variables 75
6 Bayesian inference for discrete random variables 95
7 Continuous random variables 111
8 Bayesian inference for binomial proportion 129
9 Comparing Bayesian and frequentist inferences for proportion 147
10 Bayesian inference for normal mean 169
11 Comparing Bayesian and frequentist inferences for mean 193
12 Bayesian inference for difference between means 209
13 Bayesian inference for simple linear regression 235
14 Robust Bayesian methods 261
A Introduction to calculus 275
B Use of statistical tables 295
C Using the included minitab macros 307
D Using the included R functions 317
E: Answers to selected exercises 329
References 349
Index 351
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