ABSTRACT

As in classical regression, Bayesian regression models are formulated by specifying a sampling distribution for the data (which we also loosely term the likelihood) and then a form of relationship between the assumed distribution of the response variable and any explanatory variables. The only difference is that we also specify prior distributions for the regression coefficients and any other unknown (nuisance) parameters. As we will see in this chapter, there are several advantages to a Bayesian approach, however, such as it being relatively straightforward to include parameter restrictions, use non-linear models, “robustify” against outliers, make predictions and inferences about functions of regression parameters, and handle missing data.