Introduction to Bayesian Statistics

In this brief introductory chapter, we sought to inform readers new to Bayesian statistics about the fundamental concepts in Bayesian analyses. The most important take-home messages to remember are that in Bayesian statistics, the analysis starts with an explicit formulation of prior beliefs that are updated with the observed data to obtain a posterior distribution. The posterior distribution is then used to make inferences about probable values of a given parameter (or set of parameters). Furthermore, Bayes Factors allow for comparison of non-nested models, and it is possible to compute the amount of support for the null hypothesis, which cannot be done in the frequentist framework. Subsequent chapters in this volume make use of Bayesian methods for obtaining posteriors of parameters of interest, as well as Bayes Factors.