Talk Title
Hamiltonianizing a Piecewise Deterministic Markov Process: A Bouncy Particle Sampler with "Inertia"
Abstract
The bouncy particle sampler is among the most prominent examples of piecewise deterministic Markov process samplers, a state-of-the-art paradigm in Bayesian computation. Inspired by recent connections to the Hamiltonian Monte Carlo paradigm, we present a Monte Carlo algorithm intimately related to the bouncy particle sampler but relying on Hamiltonian-like deterministic dynamics to generate a piecewise linear trajectory similar to the bouncy particle sampler’s. However, changes in its velocity occur deterministically in the manner of Hamiltonian dynamics, dictated by the auxiliary "inertia" parameter we introduce. We show that the proposed dynamics, while technically non-Hamiltonian, share the key properties of time-reversibility, energy conservation, and volume preservation. Together, these enable its use as a valid Metropolis proposal mechanism. We further establish that the dynamics, when combined with periodic refreshment of the inertia parameter, converge to the bouncy particle sampler in the limit of increasingly frequent refreshment. The dynamics can be simulated exactly on log-concave target distributions, easily accommodate parameter constraints, and require minimal tuning, yielding an efficient rejection-free sampling algorithm on a range of target distributions. We call this algorithm the Hamiltonian bouncy particle sampler, and demonstrate its competitive performance on high dimensional real-data target distributions.
Bio
