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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Quasi-stationary Monte Carlo and the ScaLE Algorithm
AU - Pollock, Murray
AU - Fearnhead, Paul
AU - Johansen, Adam M.
AU - Roberts, Gareth O.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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.
AB - 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.
KW - stat.ME
KW - stat.CO
U2 - 10.1111/rssb.12365
DO - 10.1111/rssb.12365
M3 - Journal article
VL - 82
SP - 1167
EP - 1221
JO - Journal of the Royal Statistical Society: Series B (Statistical Methodology)
JF - Journal of the Royal Statistical Society: Series B (Statistical Methodology)
SN - 1369-7412
IS - 5
ER -