Making Recursive Bayesian Inference Accessible

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.

Multistate Ornstein-Uhlenbeck approach for practical estimation of movement and resource selection around central places

“…partial pooling) is needed. Further, we demonstrated how recursive Bayesian estimation can be particularly useful in estimating complex, computationally demanding hierarchical movement models (Lunn et al, 2013; Hooten et al, 2016; Hooten and Hefley, 2019; Hooten et al, 2019).…”

Hierarchical computing for hierarchical models in ecology

“…For the data model to cancel in the numerator and denominator of the MH ratio (10), the proposals θ j ( * ) should be independent draws from the first‐stage posterior distributions for θ j . Thus, in practice, we sample θ j ( * ) randomly with replacement from the first‐stage Markov chains so that the samples are uncorrelated (Hooten et al., 2020; Lunn et al., 2013).…”

“…(2013), leverages the properties of Markov chain Monte Carlo (MCMC) sampling (Gelfand & Smith, 1990) to lessen the computational burden of fitting hierarchical models. The authors used RB to reconcile the results of several independent studies in a meta‐analysis (Lunn et al., 2013), and the method has been applied in ecological contexts to facilitate online updating (Hooten et al., 2020), model individual and group variation in physiological measurements (Hooten & Heey, 2019), and scale movement and resource‐selection models from individuals to populations (Gerber et al., 2018; Hooten et al., 2016). While not unique to ecology, RB is a natural computational technique for ecologists to consider because the RB framework mirrors many ecological study designs and hierarchical models.…”

Accumulating evidence in ecology: Once is not enough

“…Under this approach to modeling, the accumulation of evidence becomes a problem of updating estimates of key parameters as new data become available. Methods referred to as Recursive Bayes provide a natural approach for this sort of updating (see Hooten et al, ), although we still recommend the scientific step of comparing predictions with observations as a means of determining whether the general model itself is providing a reasonable approximation of underlying ecological processes (see Dietze et al, ). Thus, other approaches to accumulating evidence may be useful, in addition to the one that we propose.…”

“…Texts on statistical design reflect the single study emphasis, typically focusing on a design criterion (e.g., maximize test power) for single experiments or sets of observations (see Nelder, ). In contrast, we have seen relatively few formal efforts to draw inferences from evidence accumulated across multiple studies, and very few to design sequences of studies with a focus on accumulated evidence (but see Chaloner & Verdinelli, ; Dietze et al, ; Hooten, Johnson, & Brost, ). “This emphasis on the isolated study, with the corresponding lack of emphasis of problems of combining information from many experiments, is, I believe, an unsatisfactory feature of much statistical writing” (Nelder, ).…”