Understanding Computational Bayesian Statistics
Providing a solid grounding in statistics while uniquelycovering the topics from a Bayesian perspective, UnderstandingComputational Bayesian Statistics successfully guides readersthrough this new, cutting-edge approach. With its hands-ontreatment of the topic, the book shows how samples can be drawnfrom the posterior distribution when the formula giving its shapeis all that is known, and how Bayesian inferences can be based onthese samples from the posterior. These ideas are illustrated oncommon statistical models, including the multiple linear regressionmodel, the hierarchical mean model, the logistic regression model,and the proportional hazards model.
The book begins with an outline of the similarities anddifferences between Bayesian and the likelihood approaches tostatistics. Subsequent chapters present key techniques for usingcomputer software to draw Monte Carlo samples from the incompletelyknown posterior distribution and performing the Bayesian inferencecalculated from these samples. Topics of coverage include:
- Direct ways to draw a random sample from the posterior byreshaping a random sample drawn from an easily sampled startingdistribution
- The distributions from the one-dimensional exponentialfamily
- Markov chains and their long-run behavior
- The Metropolis-Hastings algorithm
- Gibbs sampling algorithm and methods for speeding upconvergence
- Markov chain Monte Carlo sampling
Using numerous graphs and diagrams, the author emphasizes astep-by-step approach to computational Bayesian statistics. At eachstep, important aspects of application are detailed, such as how tochoose a prior for logistic regression model, the Poissonregression model, and the proportional hazards model. A related Website houses R functions and Minitab macros for Bayesian analysisand Monte Carlo simulations, and detailed appendices in the bookguide readers through the use of these software packages.
Understanding Computational Bayesian Statistics is anexcellent book for courses on computational statistics at theupper-level undergraduate and graduate levels. It is also avaluable reference for researchers and practitioners who usecomputer programs to conduct statistical analyses of data and solveproblems in their everyday work.
336 pages; ISBN 9781118209929
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Title: Understanding Computational Bayesian Statistics
Author: William M. Bolstad
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