Bayesian models are naturally equipped to provide recursive inference 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 previous data. Recursive Bayesian methods include two main approaches that we refer to as Prior- and Proposal-Recursive Bayes. Prior-Recursive Bayes uses Bayesian updating, fitting models to partitions of data sequentially, and provides a convenient way to accommodate new data as they become available. Prior-Recursive Bayes uses the posterior from the previous stage as the prior in the new stage based on the latest data to update inference and forecasts, but is difficult to implement exactly in practice. By contrast, Proposal-Recursive Bayes is intended for use with hierarchical Bayesian models and relies on a set of transient priors in first stage independent analyses of the data partitions. The second stage of Proposal-Recursive Bayes uses the posterior distributions from the first stage as proposals in a simplified MCMC algorithm that results in computational improvements.
Results/Conclusions
We combine Prior- and Proposal-Recursive concepts in a framework that can be used to fit any Bayesian model exactly and more efficiently. While our method can be applied to fit a wide range of Bayesian models, we demonstrate it by analyzing ecological survey data of Steller sea lions at a set of rookeries over several years using online Bayesian updating to refine our forecasts as new data arrive. Overall, our new approach has implications for big data, streaming data, and optimal adaptive design strategies based on forecasts. Although our focus for this talk is on forecasting, our method can also be used to improve computational efficiency when fitting models that are notoriously computationally intensive such as geostatistical models.