Leave Pima Indians alone: binary regression as a benchmark for Bayesian computation

TL;DR

This paper critically examines the common practice of using binary regression as a benchmark for Bayesian computational methods, analyzing the effectiveness of various algorithms through extensive numerical experiments.

Contribution

It provides a comprehensive review of Bayesian computation methods applied to binary regression and questions the reliability of this benchmark for evaluating new approaches.

Findings

Some algorithms outperform expectations in certain scenarios

Conventional wisdom about algorithm effectiveness may be challenged

Implications extend to variable selection and other models

Abstract

Abstract. Whenever a new approach to perform Bayesian computation is introduced, a common practice is to showcase this approach on a binary regression model and datasets of moderate size. This paper discusses to which extent this practice is sound. It also reviews the current state of the art of Bayesian computation, using binary regression as a running example. Both sampling-based algorithms (importance sampling, MCMC and SMC) and fast approximations (Laplace and EP) are covered. Extensive numerical results are provided, some of which might go against conventional wisdom regarding the effectiveness of certain algorithms. Implications for other problems (variable selection) and other models are also discussed.