Premium
Gibbs flow for approximate transport with applications to Bayesian computation
Author(s) -
Heng Jeremy,
Doucet Arnaud,
Pokern Yvo
Publication year - 2021
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12404
Subject(s) - monte carlo method , statistical physics , mathematics , distribution (mathematics) , conditional probability distribution , gibbs sampling , computation , flow (mathematics) , ordinary differential equation , metropolis–hastings algorithm , bayesian probability , mathematical analysis , differential equation , physics , algorithm , markov chain monte carlo , geometry , statistics
Abstract Let π 0 and π 1 be two distributions on the Borel space ( R d , B ( R d ) ) . Any measurable function T : R d→R dsuch that Y = T ( X ) ∼ π 1if X ∼π 0is called a transport map from π 0 to π 1 . For any π 0 and π 1 , if one could obtain an analytical expression for a transport map from π 0 to π 1 , then this could be straightforwardly applied to sample from any distribution. One would map draws from an easy‐to‐sample distribution π 0 to the target distribution π 1 using this transport map. Although it is usually impossible to obtain an explicit transport map for complex target distributions, we show here how to build a tractable approximation of a novel transport map. This is achieved by moving samples from π 0 using an ordinary differential equation with a velocity field that depends on the full conditional distributions of the target. Even when this ordinary differential equation is time‐discretised and the full conditional distributions are numerically approximated, the resulting distribution of mapped samples can be efficiently evaluated and used as a proposal within sequential Monte Carlo samplers. We demonstrate significant gains over state‐of‐the‐art sequential Monte Carlo samplers at a fixed computational complexity on a variety of applications.