Current Research

I work in the area of statistical inference and some of the computational problems that arise when we want to apply statistical methodology. Most of my recent work is in the area of Bayesian inference where the computational challenges typically involve the need to evaluate integrals.

Bayesian Inference

Consider a situation where we have specified a sampling model, a proper prior for the model parameter and these are the only ingredients, i.e., we do not specify a loss or utility function. The principle of conditional probability, as expressed via Bayes Theorem, tells us that any probability statements we make after seeing the data must be based on the posterior. This does not tell us, however, what form inferences should take. For this we need additional requirements that we want inferences to satisfy. My research is concerned with what these should be when we have a proper prior and has lead to consideration of the measurement of the concept of surprise, invariance of inferences under reparameterizations, and optimality of Bayesian inferences with respect to repeated sampling behavior.

Model Checking and Checking for Prior-data Conflict

A common objection to Bayesian inference is the fact that the prior represents the subjective beliefs of the statistician or analyst. In many contexts we don't want inferences to depend on the particular analyst. Bayesians often respond to this by pointing out that the sampling model is also a subjective choice made by the statistician. For many scientific analyses , the objections concerning the subjective nature of the choices made by the analyst, and this applies both to the sampling model and the prior, seem quite sensible to me. The way out of this dilemma for me is through checking that the sampling model makes sense in light of the data collected and that, when the sampling model makes sense, that there is no prior-data conflict. The sampling model makes sense when there is at least one distribution in the model for which the observed data is not surprising. Then, when this is the case, there is a prior-data conflict when the prior places its mass primarily on distributions in the model for which the observed data is surprising. Model failure is very serious as it makes us doubt the validity of the inferences drawn. The existence of a prior-data conflict can also lead us to doubt the validity of our inferences but, provided we have enough data, its effects can be ignored. For this reason we should check separately for model error and for prior-data conflict.

Integration