Bayesian Risk Management

Chapter 3Model Uncertainty

In addition to the risk that unknown model parameters are imperfectly known, there is the risk that a model has been incorrectly specified, meaning that its form does not conform to the process generating the observed data. (Though we are skeptical of the classical time series notion of an ultimate “data-generation process” operative in nature, we retain use of the term as a placeholder for the reality that is imperfectly captured by our models.) Decisions about model form include the selection of conditioning data series, as well as a variety of choices about the functional form of the joint probability distribution. Though analysts will regularly audition a variety of model specifications in the course of analyzing a data set, it is rare that the final model specification is closely interrogated. As a result, a highly subjective and perhaps arbitrary choice is allowed to stand virtually beyond criticism in many, if not most, empirical investigations. Not only does this call into question the supposed objectivity of classical statistics, but it also arouses interest as to whether methods that accept subjectivity as an irreducible fact of statistical modeling can shed greater light on the relative merits of different model specifications.

Classical statistics tends to imagine model selection as a reduction of a highly inclusive “encompassing” model to a minimal subset of covariates via a series of hypothesis tests (Hendry and Nielsen 2007). Such an ...