Making Recursive Bayesian Inference Accessible

TL;DR

This paper introduces a combined recursive Bayesian inference method that simplifies and improves Bayesian analysis for complex models, big data, and streaming data scenarios.

Contribution

It merges prior- and proposal-recursive Bayesian methods to enable flexible, efficient inference for any Bayesian model, often with computational benefits.

Findings

Successfully applied to two case studies

Enhances Bayesian inference for big and streaming data

Offers computational improvements over existing methods

Abstract

Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior distributions resulting from former studies. Two existing Recursive Bayesian methods are: Prior- and Proposal-Recursive Bayes. Prior-Recursive Bayes uses Bayesian updating, fitting models to partitions of data sequentially, and provides a way to accommodate new data as they become available using the posterior from the previous stage as the prior in the new stage based on the latest data. Proposal-Recursive Bayes is intended for use with hierarchical Bayesian models and uses a set of transient priors in first stage independent analyses of the data partitions. The second stage of Proposal-Recursive Bayes uses the posteriors from the first stage as proposals in an MCMC algorithm to fit the full model. We combine Prior- and Proposal-Recursive concepts to fit any Bayesian model, and often with computational improvements. We demonstrate our method with two case studies. Our approach has implications for big data, streaming data, and optimal adaptive design situations.