Validity-Preservation Properties of Rules for Combining Inferential Models
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:286-294, 2019.
An inferential model encodes the data analyst’s degrees of belief about an unknown quantity of interest based on the observed data, posited statistical model, etc. Inferences drawn based on these degrees of belief should be reliable in a certain sense, so we require the inferential model to be valid. The construction of valid inferential models based on individual pieces of data is relatively straightforward, but how to combine these so that the validity property is preserved? In this paper we analyze some common combination rules with respect to this question, and we conclude that the best strategy currently available is one that combines via a certain dimension reduction step before the inferential model construction.