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 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.