Bayesian Statistics and Marketing, 2nd Edition

6Model Choice and Decision Theory

Abstract

This chapter discusses Bayesian Model Choice and decision theory. Bayesian Model Choice involves various approaches to computing the posterior probability of a model. Posterior model probabilities are useful in comparing two or more competing models or in the choice from a class of models. While there are some methods which can use standard MCMC output to approximate these probabilities, most problems require additional computations for accurate evaluation of posterior probabilities. Sections 6.1–6.9 introduce various methods for computation of model probabilities and compare some of the most useful methods in the context of a model comparison motivated by the multinomial probit model. Many marketing problems suggest a natural decision problem (such as profit‐maximization) so that there is more interest in non‐trivial applications of decision theory. Sections 6.10 and 6.11 introduce a Bayesian decision‐theoretic approach to marketing problems and provide an example by considering the valuation of disaggregate sample information.

Most of the recent Bayesian literature in marketing emphasizes the value of the Bayesian approach to inference, particularly in situations with limited information. Bayesian inference is only a special case of the more general Bayesian decision‐theoretic approach. Bayesian Decision Theory has two critical and separate components: 1. a loss function and 2. the posterior distribution. The loss function associates ...