Bayesian Model Diagnostics with Order Restrictions on Cell Probabilities

• Activity Number: 350 - Bayesian Modeling and Simulation
• Type: Contributed
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistical Computing
• Author(s): Xinyu Chen*
• Companies: Worcester Polytechnic Institute
• Keywords: Bayesian computation; LPML; Multinomial counts; Small areas; Unimodal order restrictions

Abstract

We study Bayesian diagnostics for multinomial counts from small areas. Within each area, the cell probabilities are ordered (e.g. unimodal ordering). Specifically we consider Bayesian diagnostics for a multinomial Dirichlet model with order restriction which shares a common effect among areas and make model diagnostics for it. The log pseudo marginal likelihood (LPML) is a well-known Bayesian criterion for comparing models. Since the order restriction significantly increases the difficulty, we develop an algorithm to compute LPML. We use a special- designed importance function to increase the efficiency of Monte Carlo integration, thereby gaining a higher precision for estimations of LPML. The proposed methodology is applied to a case study of body mass index (BMI).