Quality quandaries: A gentle introduction to Bayesian statistics

摘要

In this article, we illustrated some basics of performing a Bayesian analysis. We showed how Bayesian statistics combines data with auxiliary information through a prior distribution to obtain a posterior distribution. The posterior distribution is then used to summarize what we know about a model parameter expressed as a point estimate and an interval estimate. Additionally, we showed how posterior distributions of functions of the parameter are obtained. Here, we considered a single parameter but more complex situations involving a vector of parameters are straightforward to handle. Also, a Bayesian analysis can incorporate multiple sources of data and multiple models in a simultaneous analysis. We will encounter such situations in future Quality Quandaries columns; see also Andreon and Weaver (2015) and Hamada et al. (2008) for other examples of Bayesian analyses.