Quasi-stationary Monte Carlo and the ScaLE Algorithm

Pollock, Murray and Fearnhead, Paul and Johansen, Adam M. and Roberts, Gareth O. (2019) Quasi-stationary Monte Carlo and the ScaLE Algorithm. Journal of the Royal Statistical Society. Series B: Statistical Methodology. (In Press)

[img]
Text (SCALE_accepted)
SCALE_accepted.pdf - Accepted Version
Restricted to Repository staff only until 1 January 2050.
Available under License Creative Commons Attribution.

Download (3MB)

Abstract

This paper introduces a class of Monte Carlo algorithms which are based upon simulating a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current Markov chain Monte Carlo methods which simulate a Markov chain whose stationary distribution is the target. We show how to approximate distributions of interest by carefully combining sequential Monte Carlo methods with methodology for the exact simulation of diffusions. The methodology introduced here is particularly promising in that it is applicable to the same class of problems as gradient based Markov chain Monte Carlo algorithms but entirely circumvents the need to conduct Metropolis-Hastings type accept/reject steps whilst retaining exactness: the paper gives theoretical guarantees ensuring the algorithm has the correct limiting target distribution. Furthermore, this methodology is highly amenable to big data problems. By employing a modification to existing naıve sub-sampling and control variate techniques it is possible to obtain an algorithm which is still exact but has sub-linear iterative cost as a function of data size.

Item Type:
Journal Article
Journal or Publication Title:
Journal of the Royal Statistical Society. Series B: Statistical Methodology
Subjects:
ID Code:
82049
Deposited By:
Deposited On:
07 Oct 2016 10:38
Refereed?:
Yes
Published?:
In Press
Last Modified:
26 Mar 2020 02:47