Bayesian Model Comparison and Validation

Bayesian econometrics provides a tidy theory and practical methods of comparing and combining several alternative, completely specified models for a common dataset, which is reviewed in Section I. Dale J. Poirier (1988) provides a more extensive introduction. It is always possible that none of the specified models describes important aspects of the data well. The investigation of this possibility, a process known as model validation or model specification checking, is an important part of applied econometric work. Bayesian theory and practice for model validation are developed less well. A well-established Bayesian literature, beginning with George E. P. Box (1980) and summarized in Roderik J. Little (2006), argues that non-Bayesian methods are essential in model validation. This line of thought persists in Bayesian econometrics as well, (see recent texts by Tony Lancaster 2004 and John Geweke 2005). Section II reviews these methods. This essay suggests an alternative, fully Bayesian method of model validation based on the concept of incomplete models, introduced in Section III. The concluding section of this essay argues that this method is also strategically advantageous in applied Bayesian econometrics.