An expected utility approach to influence diagnostics

We consider the problem of defining the influence of a set of observations in a parametric modeling framework. An expected utility approach, motivated by the amount of information to be gained from an experiment, is developed with regard to the parameter of interest. In some linear model cases simple closed-form expressions for our criterion may be found. In more complicated settings an adaptive Monte Carlo integration technique known as the Gibbs sampler provides a natural framework for evaluating the influence diagnostic. We demonstrate that the influence diagnostic obtained performs well in flagging aberrant subsets of the data, exemplified in the cases of a two-stage linear model, a hierarchical model, and a nonlinear Michaelis-Menten model.