Tuesday, Aug 5: 10:30 AM - 12:20 PM
0576
Topic-Contributed Paper Session
Music City Center
Room: CC-202B
Modern computing environments continue to improve allowing us to fit models to data faster than
ever before. In particular, multi-processor and distributed computing resources have become
widely available in academics, agencies, and industry, and the computing cores per machine
continues to increase. More emphasis on parallel computing using graphical processing units
(GPUs) and the demand for massive high-performance computing centers driven by the large
language model (LLM) training needs of the AI-based industry has led to unprecedented
accessibility of such resources.
Ecological and environmental data sets continue to grow in size and complexity due to
technological advances and increased interest. Recursive (i.e., multi-stage) approaches for fitting
statistical models often allow us to leverage modern parallel computing environments and they
have proliferated in the Bayesian and machine learning fields. Despite these advancements
however, many approaches are either too complicated or too narrowly applicable for ecologists
and environmental scientists to adopt. Fortunately, ongoing developments in recursive statistical
computing have led to simple and intuitive methods that can be refined and generalized with
ease. Combined with readily available software for parallelization, these new recursive computing
approaches have enabled practitioners and led to improvements in scientific inquiry based on
large data sets. Recursive computing methods have also inspired new approaches to formulate
statistical models that can be both more general and economize implementation at the same
time.
This proposed invited session comprises statisticians across a range of career stages who work on
ecological and environmental applications. Each will present new methodology in recursive
Bayesian computing, developing ways to make implementation of statistical models scalable and
accurate and demonstrating the approaches using a variety of ecological and environmental data
sets.
Bayesian
Markov Chain Monte Carlo
Ecology
Environment
Spatial
Hierarchical Models
Applied
Yes
Main Sponsor
Section on Statistics and the Environment
Co Sponsors
Biometrics Section
Section on Bayesian Statistical Science
Presentations
Recursive Bayesian inference is an important tool for applications in which data arrives sequentially and updated parameter estimates are desired each time data arrives. Models for which the posterior distribution is estimated via Markov chain Monte Carlo (MCMC) can use Prior-Proposal-Recursive Bayes (PPRB) to resample existing posterior samples using the likelihood of the new data. Like all filtering methods, if applied many times PPRB will eventually converge to sampling from a degenerate distribution, limiting its usefulness for repeated application in longitudinal data settings. We present a sampling strategy for recursive Bayesian inference that extends PPRB to avoid the eventual tendency towards degeneracy by the addition of a transition kernel step run in parallel on each filtered sample. We show that this sampler improves upon PPRB by producing samples from the target posterior distribution that will not tend towards degeneracy. Additionally, we compare the performance of the proposed sampler to other streaming samplers for recursive inference and present an application to Ecological species count data.
Keywords
Recursive Bayes
Distributed MCMC
Streaming Data
The surge in access to computing resources has attracted attention toward the development of algorithms that can run efficiently on multi-core processing units or in distributed computing environments. In the context of Bayesian inference, MCMC still remains the most reliable and widely applicable algorithm to characterize posterior distributions, however its Markovian nature imposes challenges when it comes to parallelization. Running independent chains is inefficient due to the need to discard a fixed number of observations as burn in, while parallelizing a single chain leads to additional communication costs at every iteration. To circumvent both of these issues, multistage approaches have been proposed, where a sample from a computationally convenient and parallel friendly approximation of the posterior distribution is obtained and later corrected using an importance sampling or Metropolis-Hastings post-processing step. In this work, propose an extension of pre-existing multistage approaches, showcasing the effectiveness of the resulting algorithm considering both simulated experiments and real data.
Keywords
Bayesian inference
embarrassingly parallel MCMC
Gaussian process
Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating batches of data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. Implementation typically proceeds via a sequence of "transient" posteriors characterized by samples obtained using acceptance/rejection algorithms in which draws from one posterior in the sequence are used as proposals for the next. While straightforward to implement, such filtering approaches suffer from particle depletion, degrading each sample's ability to represent its target posterior. Generating proposals from smoothed versions of the transient posterior's empirical sampling distributions can alleviate particle depletion, but the efficiency of such an approach can be extremely limited for moderate to high dimensional parameter spaces. We introduce new tools for smoothed recursive Bayesian inference in the form of blocking and generalized elliptical slice samplers that ensure satisfactory effective sample sizes throughout the sequence of transient posterior samples. We apply the method to satellite imagery to classify forest vegetation in New Mexico.
Keywords
recursive Bayes
generalized elliptical slice sampler
satellite imagery
vegetation cover
Bayesian analyses of large spatio-temporal data are hindered by the computational expense required to implement Markov chain Monte Carlo (MCMC) algorithms. A common solution is for researchers to reduce the dimensionality by making simplifying assumptions in the spatial and/or temporal structure. While this increases computational efficiency, it comes at the cost of model flexibility. Alternatively, we propose a multi-stage MCMC approach that
permits Bayesian analysis of the full model. The use of parallel computing alleviates the computational expense associated with large space-time data, making this approach scalable and generalizable to a flexible class of spatio-
temporal models. This work is motivated by spatio-temporal ordinal data from the US Drought Monitor. This weekly data product records drought conditions across the United States as one of six ordered levels. We develop a Bayesian
spatio-temporal ordinal model for modeling and forecasting drought conditions, and we fit this model with the proposed multi-stage MCMC approach.
Keywords
Bayesian computing
MCMC
parallel computing
spatial
environmental
Bayesian point process models are commonly used to analyze presence-only data in ecology. Current methods for fitting these models are computationally expensive because they require numerical quadrature and algorithm supervision. We propose a flexible and efficient multi-stage Bayesian approach to fitting point process models that leverages parallel computing resources to estimate coefficients and predict total abundance. We show how this method can be extended to study designs with compact observation windows and allows for posterior prediction in unobserved areas, which can be used for downstream analyses. We demonstrate this approach using a simulation study and on imagery data from aerial surveys to learn spatially explicit abundance of harbor seals in Johns Hopkins Inlet, an important glacial fjord in Alaska.
Keywords
spatial point process
recursive Bayes
species distribution modeling
presence-only data
parallel processing
Markov Chain Monte Carlo