Review Seminar: Jakob Torgander

Opponent Mattias Villani, Department of Statistics, Stockholm University

Topic SimplexMCMC: An Auxiliary-Variable Framework for Mixed Discrete–Continuous Posterior Distributions

Abstract This paper introduces SimplexMCMC, a Markov chain Monte Carlo (MCMC) framework for sampling from mixed continuous-discrete posterior distributions. Discrete sampling is reformulated as sampling from the interior of the probability simplex, leading to an auxiliary-variable MCMC construction that admits the target discrete distribution as its stationary distribution. The framework is extended to Bayesian models with mixed discrete and continuous parameters and admits an HMC-based instantiation that makes use of the Gumbel–Softmax distribution. This instantiation, referred to as Relaxed Discrete Hamiltonian Monte Carlo (RD-HMC), provides a practical algorithm for approximate inference in mixed continuous-discrete models. Correctness of the SimplexMCMC framework is established through theoretical convergence results, and the practical behaviour of RD-HMC is assessed empirically on simulated and real data.