Abstract
MCMC algorithms such as Metropolis--Hastings algorithms are slowed down by the computation of complex target distributions as exemplified by huge datasets. We offer a useful generalisation of the Delayed Acceptance approach, devised to reduce such computational costs by a simple and universal divide-and-conquer strategy. The generic acceleration stems from breaking the acceptance step into several parts, aiming at a major gain in computing time that out-ranks a corresponding reduction in acceptance probability. Each component is sequentially compared with a uniform variate, the first rejection terminating this iteration. We develop theoretical bounds for the variance of associated estimators against the standard Metropolis--Hastings and produce results on optimal scaling and general optimisation of the procedure.
Original language | English |
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Pages (from-to) | 103-128 |
Number of pages | 25 |
Journal | Foundations of Data Science |
Volume | 1 |
Issue number | 2 |
Early online date | 19 Mar 2019 |
DOIs | |
Publication status | Published - 1 Jun 2019 |