Inferential Models: A Framework for Valid Prior-Free Probabilistic Inference

• Activity Number: 322
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Chuanhai Liu*+
• Companies: Purdue University
• Keywords: Prediction ; Optimality ; Paradox-free ; Marginalization ; Conditional inference ; Auxiliary variables

Abstract

Conventional schools of thought on statistical inference are challenged by very high dimensional problems and irreproducibility of published research. The Inferential Model (IM) framework, proposed most recently for prior-free probabilistic inference with desirable frequency properties, could perhaps be a promising alternative. The basic idea of IMs is to associate the observed data and unknown quantities/parameters with predictable quantities, called auxiliary variables. IMs produce genuine probabilistic results for scientific inference by predicting unobserved auxiliary variables using predictive random sets conditioning on observed auxiliary variables. This talk introduces IMs, including conditional IMs (CIMs) and marginal IMs (MIMs) for efficient inference, with simple illustrative examples.

This is joint work with Ryan Martin, University of Illinois at Chicago.