Nonreversible MCMC with Constraints or Discontinuities

10.12.2021 11:15 – 12:15

RESEARCH CENTER FOR STATISTICS SEMINAR / ABSTRACT

MCMC is a standard tool for sampling from unnormalised distributions, which is a common task in Bayesian inference among other settings. A key feature of practical algorithms is that they should explore the support of the target distribution rapidly. Essentially all MCMC methods in wide use are based on reversible random walks, which have an inherent tendency to backtrack in a manner characteristic of diffusions, inhibiting exploration. A recent body of work has introduced several classes of nonreversible MCMC methods based on piecewise deterministic Markov processes, which avoid diffusive backtracking. However, the formulations of these methods require connected state spaces without boundaries, as well as differentiable target densities. I will show that analogous processes can be constructed on state spaces consisting of disconnected regions with boundaries, and for target densities with discontinuities. I will illustrate the construction with sampling from the posterior distribution of the Kingman coalescent model of population genetics, whose support consists of discrete binary tree topologies as well as nonnegative, continuous branch lengths.

Lieu

Online

entrée libre