B0820
Title: Incorporating partial prior information in an inferential model
Authors: Leonardo Cella - North Carolina State University (United States) [presenting]
Abstract: Even when prior information is available in practice, it is often partial/incomplete, i.e., it does not come in the form of a fully specified probability distribution. Of course, incomplete prior information can mean many different things. On one end of the spectrum, it could be a hard/definitive constraint on some parameter of interest; on the other end, it could be structural assumptions like those commonly assumed in high-dimensional settings (e.g., sparsity); and in the middle, it could be something like a subject-matter expert saying that she is ``90\% sure that the parameter is in the interval [7,10]'' We argue that such priors can be represented without embellishment by random sets, and explore their incorporation within the Inferential Models framework, an originally prior-free approach for valid statistical inference. This incorporation is guided by desired properties, such as that validity is maintained regardless of the truthfulness of the partial prior and that correct partial priors should result in more efficient inferences.
