Auxiliary-variable Exact Hamiltonian Monte Carlo Samplers for Binary\n Distributions

2013/11/09 by Ari Pakman, Liam Paninski, Pakman, Ari +1 · 3 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1311.2166

openalex publication_date 2013/11/09 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

We present a new approach to sample from generic binary distributions, based\non an exact Hamiltonian Monte Carlo algorithm applied to a piecewise continuous\naugmentation of the binary distribution of interest. An extension of this idea\nto distributions over mixtures of binary and possibly-truncated Gaussian or\nexponential variables allows us to sample from posteriors of linear and probit\nregression models with spike-and-slab priors and truncated parameters. We\nillustrate the advantages of these algorithms in several examples in which they\noutperform the Metropolis or Gibbs samplers.\n

Citations

• The horseshoe estimator for sparse signals

Cited by

• Smoothing Out Sticking Points: Sampling from Discrete-Continuous Mixtures with Dynamical Monte Carlo by Mapping Discrete Mass into a Latent Universe
• Bayesian spike inference from calcium imaging data
• Bayesian Inference with the l1-ball Prior: Solving Combinatorial Problems with Exact Zeros

Related

• Exact Hamiltonian Monte Carlo for Truncated Multivariate Gaussians
• Exact Hamiltonian Monte Carlo for Truncated Multivariate Gaussians
• Binary Bouncy Particle Sampler
• Numerical Generalized Randomized Hamiltonian Monte Carlo for piecewise smooth target densities
• Design of Hamiltonian Monte Carlo for perfect simulation of general continuous distributions