Exact and efficient inference for Partial Bayes problems

TL;DR

This paper introduces a novel inference framework for Partial Bayes problems, providing exact and efficient solutions that improve Bayesian inference when prior information is limited, supported by theoretical and empirical evidence.

Contribution

It develops a general Inferential Model-based approach for Partial Bayes problems, offering the first exact and computationally efficient solutions in this context.

Findings

The proposed method achieves superior accuracy in numerical experiments.

Real-world applications demonstrate practical effectiveness.

The framework provides a unified approach for Partial Bayes inference.

Abstract

Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called Partial Bayes problems, in which the prior information is only partially available. Taking the recently proposed Inferential Model approach, we develop a general inference framework for Partial Bayes problems, and derive both exact and efficient solutions. In addition to the theoretical investigation, numerical results and real applications are used to demonstrate the superior performance of the proposed method.