Bayesian Modeling

Frequentist and Bayes are two general approaches in the development of statistical methods. Frequentist methods covered in this book include the familiar t confidence intervals, linear regression models, and ANOVA for testing equality of means. This chapter introduces the Bayesian approach to statistical inference by use of several illustrative examples. In the Bayes approach, one performs inference by the use of subjective probability. A prior density represents one’s initial opinion on the location of the parameter. After data is observed, by Bayes’ rule, one’s updated opinion about the parameter is expressed by the posterior distribution. One performs inference by summarizing the posterior distribution. One checks the validity of the model and predict future data by the use of the predictive distribution. The Metropolis-Hastings algorithm is introduced as a practical method to draw samples from the posterior distribution.