In this chapter, we introduce the use of R in summarizing the posterior distributions for several single-parameter models. We begin by describing Bayesian inference for a variance for a normal population and inference for a Poisson mean when informative prior information is available. For both problems, summarization of the posterior distribution is facilitated by the use of R functions to compute and simulate distributions from the exponential family. In Bayesian analyses, one may have limited beliefs about a parameter and there may be several priors that provide suitable matches to these beliefs. In estimating a normal mean, we illustrate the use of two distinct priors in modeling beliefs, and show that inferences may or may not be sensitive to the choice of prior.
KeywordsPosterior Probability Posterior Distribution Prior Distribution Posterior Density Prior Belief
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