Bayesian Model Comparison and Validation 1

Models are the venue for much of the work of the economics profession. We use them to express, compare and evaluate alternative ways of addressing important questions. Applied econometricians are called upon to engage in these exercises using data and, often, formal methods whose properties are understood in decision-making contexts. This is true of work in other sciences as well. There is an enormous literature on alternative formal approaches to these tasks, and in particular on the relative advantages of Bayesian and frequentist methods. By “Bayesian ” I mean statistical inference that reaches a conclusion by means of a conditional distribution of unknown quantities given known quantities and model specifications. This conditional distribution follows from applying Bayes’s theorem to the joint distribution of known and unknown quantities in the model specifications. Known quantities, including data, are treated as observed values of random variables. Unknown quantities, including functions of parameters and as yet unobserved data, are treated as unobserved random variables. Formal methods of model expression, comparison and evaluation that do not have these attributes are non-Bayesian. By “frequentist ” I mean a particula