Title: 

Sampling with Velocities.

Abstract:

Bayesian modeling relies on efficient techniques to perform posterior inference over complex probability distributions. Among Monte Carlo methods, two particularly efficient approaches enlarge the sampling space with velocity vectors: 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 then 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, which allows to evaluate minibatches of the data at each iteration while introducing minimal bias in the sampled distribution.