A new algorithm to compute Bayes factors of order-constrained hypotheses about multiple binomials

This paper introduces the BF-Poly-H algorithm for computing Bayes factors for binomial models that are characterized by arbitrary linear constraints. BF-Poly-H combines the simulated annealing-based integration technique of Lovász and Vempala (2006a) with Constrained Riemannian Hamiltonian Monte Carlo (CRHMC) sampling. This approach estimates the Bayes factor via a sequence of distributions that gradually anneals from a uniform distribution to the target posterior. CRHMC efficiently navigates the geometry of the constrained space at each step in the annealing process. We provide analytical results on scalability and convergence of the algorithm, alongside a suite of simulations demonstrating its performance across a broad range of scenarios. BF-Poly-H delivered accurate and precise results in all scenarios we tested. The most challenging scenario is a complicated combination of inequality and equality constraints among 100 binomials. By offering a robust solution for assessing the performance of high-dimensional and elaborately constrained binomial models, BF-Poly-H substantially expands the scope of feasible Bayesian hypothesis testing. • BF-Poly-H calculates Bayes factors for linearly-constrained binomial models. • Combines simulated annealing integration with a constrained RHMC sampler. • Handles arbitrary combinations of linear inequality and equality constraints. • Scales efficiently to high-dimensional models with 100+ binomial parameters. • Expands the scope of feasible Bayesian hypothesis tests.