Enhancing Approximate Modular Bayesian Inference by Emulating the Conditional Posterior

TL;DR

This paper introduces the ECP algorithm, an efficient emulation-based method to improve approximate modular Bayesian inference by increasing imputations and reducing computational costs, outperforming traditional approaches.

Contribution

The paper proposes the ECP algorithm that enhances the accuracy and efficiency of cut-distribution approximation in modular Bayesian analysis using emulation techniques.

Findings

ECP outperforms the traditional DS algorithm in accuracy.

ECP reduces computational costs in resource-constrained settings.

Design of experiments can improve DS algorithm performance.

Abstract

In modular Bayesian analyses, complex models are composed of distinct modules, each representing different aspects of the data or prior information. In this context, fully Bayesian approaches can sometimes lead to undesirable feedback between modules, compromising the integrity of the inference. This paper focuses on the "cut-distribution" which prevents unwanted influence between modules by "cutting" feedback. The multiple imputation (DS) algorithm is standard practice for approximating the cut-distribution, but it can be computationally intensive, especially when the number of imputations required is large. An enhanced method is proposed, the Emulating the Conditional Posterior (ECP) algorithm, which leverages emulation to increase the number of imputations. Through numerical experiment it is demonstrated that the ECP algorithm outperforms the traditional DS approach in terms of accuracy and computational efficiency, particularly when resources are constrained. It is also shown how the DS algorithm can be improved using ideas from design of experiments. This work also provides practical recommendations on algorithm choice based on the computational demands of sampling from the prior and cut-distributions.