Statistics Seminar: "A Bayesian Considers Optimal Sampling from an Information Theoretic Perspective"
Abstract: Most data analysis involves ignorable sampling; the distribution of the sampling mechanism is independent from the population values. In the context of a Bayesian analysis, this renders the sampling mechanism unimportant when computing the posterior distribution of quantities of interest. What then, if anything, would a Bayesian have to say about optimal sampling when sampling is assumed to be ignorable? I try to answer this question from an information theoretic perspective while assuming no other utility structure. I define a criterion that provides for unique optimal sampling design in very general settings. While this is theoretically encouraging, it leads to an intractable inverse problem. This is similar to the inverse problem that arises when defining reference priors in an Objective Bayesian setting.
Host: Todd Kuffner