Bayesian inference on high-dimensional multivariate binary responses

TL;DR

This paper introduces a scalable two-stage Bayesian inference method for high-dimensional multivariate binary response data, effectively handling the intractability of likelihood calculations in high dimensions, with applications in ecology.

Contribution

It proposes a novel two-stage inference approach leveraging latent Gaussian models to efficiently analyze high-dimensional binary data, improving scalability and accuracy.

Findings

Method performs well in simulations

Effective in ecological species distribution modeling

Reduces computational complexity significantly

Abstract

It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for inferences. However, algorithms for fitting such models face issues in scaling up to high dimensions due to the intractability of the likelihood, involving an integral over a multivariate normal distribution having no analytic form. Although a variety of algorithms have been proposed to approximate this intractable integral, these approaches are difficult to implement and/or inaccurate in high dimensions. Our main focus is in accommodating high-dimensional binary response data with a small to moderate number of covariates. We propose a two-stage approach for inference on model parameters while taking care of uncertainty propagation between the stages. We use the special structure of latent Gaussian models to reduce the highly expensive computation involved in joint parameter estimation to focus inference on marginal distributions of model parameters. This essentially makes the method embarrassingly parallel for both stages. We illustrate performance in simulations and applications to joint species distribution modeling in ecology.