2013/06/10 by Ari Pakman, Liam Paninski · 4 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference
paper · doi:10.1080/10618600.2013.788448
openalex publication_date 2013/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.