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. ProposalRecursive 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.
