Ari Pakman, Ph.D. Columbia University

Title: Sampling with Velocities.

Bayesian modeling relies on efficient techniques to perform posterior inference over complex probability distributions. Among Monte Carlo methods, two particularly efficient approaches rely on enlarging the sampling space with velocity variables: Hamiltonian Monte Carlo (HMC) and the Bouncy Particle Sampler (BPS). For HMC, I will first present two non-trivial distributions where the Hamiltonian equations of motion can be integrated exactly: truncated multivariate Gaussians and binary distributions. I will also present an application of these techniques to a statistical neuroscience problem. For large datasets, stochastic versions of Metropolis-Hastings samplers do not preserve the distribution. I will present a stochastic version of the BPS that solves this problem and allows to evaluate mini-batches of the data at each iteration while introducing minimal bias in the sampled distribution.