ABSTRACT
A Bayesian analysis may depend critically on the modeling assumptions that include prior, likelihood, and loss function. While a loss function is presumably a choice made in the context of particular situations, there is no harm and potentially some gain in investigating the effect on an analysis using alternative loss functions. The likelihood is supposed to represent, to some approximation, the physical process generating the data while the prior reflects subjective views about some of the assumed constructs of this process. Now a likelihood model that has been judged adequate in previous situations similar to a current one is certainly a prime candidate for modeling. It may also have been selected as the most likely when compared with several others and even passed, to a greater or lesser degree, scrutiny by a model criticism technique. However, even in such situations the statistician is still obliged to investigate its present adequacy. A way of addressing this problem is to perturb the “standard” model to a greater or lesser degree in potentially conceivable directions to determine the effect of such alterations on the analysis. While for the strict Bayesian the prior is subjective, it is common knowledge how difficult it often is to subject an investigator or even a statistician to an elicitation procedure that convincingly yields an appropriately subjective prior, even if the parameter is meaningful. As indicated previously, most often the parameter is merely an artifice to promote modeling for prediction. Hence to perturb an investigator’s prior or some standard one that appears appropriate is also sensible.
