Exact Hamiltonian Monte Carlo for Truncated Multivariate Gaussians

• Activity Number: 278
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ari Pakman*+ and Liam Paninski
• Companies: Columbia University and Columbia University
• Keywords: Hamiltonian Monte Carlo ; Bayesian Analysis ; Multivariate Gaussian ; Truncated distributions ; Neuroscience

Abstract

We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be integrated exactly and there are no parameters to tune. The algorithm mixes faster and is more efficient than Gibbs sampling. The runtime depends on the number and shape of the constraints but the algorithm is highly parallelizable. In many cases, we can exploit special structure in the covariance matrices of the untruncated Gaussian to further speed up the runtime. A simple extension of the algorithm permits sampling from distributions whose log-density is piecewise quadratic, as in the "Bayesian Lasso" model. We illustrate the usefulness of this algorithm in several applications.