Inferential models and restricted spaces

Duncan Ermini Leaf, Purdue University

Abstract

Inferential models produce posterior-like evidence distributions that are calibrated for frequentist inference without requiring prior distributions. This dissertation introduces methods for building inferential models when there are restrictions on either the sample space or the parameter space of a probability model. Following a review of relevant theory, the elastic method is introduced for handling parameter space constraints. This method is demonstrated with two univariate examples from high-energy physics: inference about a non-negative quantity measured with Normally distributed error and inference about the signal rate of a Poisson count with a known background rate. Existing methods for forming confidence intervals in these two examples do not provide the probabilistic evidence measure for inference that is afforded by the IM framework. An inferential model for constrained regression with Poisson data is also developed using the elastic method and demonstrated with an example from actuarial science. Previous work with this example focused on estimation. Here, the goal is probabilistic inference about estimates or more general hypotheses. Finally, data-dependent hypotheses are formulated as a source of sample space restrictions. An inferential model is introduced for the hypothesis of a positive mean in a subgroup with the best sample mean response. The bias due to the selection procedure is implicitly handled by the inferential model. This approach is then extended to an example from clinical trials where new sample data are collected after subgroup selection.

Degree

Ph.D.

Advisors

Liu, Purdue University.

Subject Area

Statistics

COinS