Sampling approaches in Bayesian computational statistics with R

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Title: Sampling approaches in Bayesian computational statistics with R
Author: Sun, Wenwen
Abstract: Bayesian analysis is definitely different from the classic statistical methods . Although , both of them use subjective ideas , it is used in the selection of models in the classic statistical methods , rather than as an explicit part in Bayesian models , which allows the combination of subjective ideas with the data collected , update the prior information and improve inferences . Drastic growth of Bayesian applications indicates it becomes more and more popular , because the advent of computational methods (e .g . , MCMC ) renders sophisticated analysis . In Bayesian framework , the flexibility and generality allows it to cope with very complex problems . One big obstacle in earlier Bayesian analysis is how to sample from the usually complex posterior distribution . With modern techniques and fast -developed computation capacity , we now have tools to solve this problem . We discuss Acceptance -Rejection sampling , importance sampling and then the MCMC methods . Metropolis -Hasting algorithm , as a very versatile , efficient and powerful simulation technique to construct a Markov Chain , borrows the idea from the well -known acceptance -rejection sampling to generate candidates that are either accepted or rejected , but then retains the current values when rejection takes place (1 ) . A special case of Metropolis -Hasting algorithm is Gibbs Sampler . When dealing with high dimensional problems , Gibbs Sampler doesn’t require a decent proposal distribution . It generates the Markov Chain through univariate conditional probability distribution , which greatly simplifies problems . We illustrate the use of those approaches with examples (with R codes ) to provide a thorough review . Those basic methods have variants to deal with different situations . And they are building blocks for more advanced problems . This report is not a tutorial for statistics or the software R . The author assumes that readers are familiar with basic statistical concepts and common R statements . If needed , a detailed instruction of R programming can be found in the Comprehensive R Archive Network (CRAN ) : http : / /cran .R -project .org
URI: http : / /hdl .handle .net /2152 /ETD -UT -2009 -12 -611
Date: 2010-08-27


Sampling approaches in Bayesian computational statistics with R. Master's thesis, The University of Texas at Austin. Available electronically from http : / /hdl .handle .net /2152 /ETD -UT -2009 -12 -611 .

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