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Accelerating delayed-acceptance Markov chain Monte Carlo algorithms

Wiqvist, Samuel LU ; Picchini, Umberto LU and Forman, Julie Lyng (2018)
Abstract
Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution, via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and computationally cheaper version) of said distribution. DA-MCMC accelerates MCMC sampling in complex applications, while still targeting the exact distribution. We design a computationally faster DA-MCMC algorithm, which samples from an approximation of the target distribution. As a case study, we also introduce a novel stochastic differential equation model for protein folding data. We consider parameters inference in a Bayesian setting where a surrogate likelihood function is introduced in the... (More)
Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution, via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and computationally cheaper version) of said distribution. DA-MCMC accelerates MCMC sampling in complex applications, while still targeting the exact distribution. We design a computationally faster DA-MCMC algorithm, which samples from an approximation of the target distribution. As a case study, we also introduce a novel stochastic differential equation model for protein folding data. We consider parameters inference in a Bayesian setting where a surrogate likelihood function is introduced in the delayed-acceptance scheme. In our applications we employ a Gaussian process as a surrogate likelihood, but other options are possible. In our accelerated algorithm the calculations in the "second stage" of the delayed-acceptance scheme are reordered in such as way that we can obtain a significant speed-up in the MCMC sampling, when the evaluation of the likelihood function is computationally intensive. We consider both simulations studies, and the analysis of real protein folding data. Simulation studies for the stochastic Ricker model and the novel stochastic differential equation model for protein-folding data, show that the speed-up is highly problem dependent. The more involved the computations of the likelihood function are, the higher the acceleration becomes when using our algorithm. Inference results for the standard delayed-acceptance algorithm and our approximated version are similar, indicating that our approximated algorithm can return reliable Bayesian inference. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Working Paper
publication status
unpublished
subject
keywords
Bayesian inference, Gaussian process, pseudo marginal MCMC, protein folding, Stochastic differential equation
pages
55 pages
language
English
LU publication?
yes
id
5f10bad7-774b-4ad5-b2a7-ac966615f612
date added to LUP
2018-06-18 13:12:28
date last changed
2018-11-21 21:40:25
@misc{5f10bad7-774b-4ad5-b2a7-ac966615f612,
  abstract     = {Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution, via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and computationally cheaper version) of said distribution. DA-MCMC accelerates MCMC sampling in complex applications, while still targeting the exact distribution. We design a computationally faster DA-MCMC algorithm, which samples from an approximation of the target distribution. As a case study, we also introduce a novel stochastic differential equation model for protein folding data. We consider parameters inference in a Bayesian setting where a surrogate likelihood function is introduced in the delayed-acceptance scheme. In our applications we employ a Gaussian process as a surrogate likelihood, but other options are possible. In our accelerated algorithm the calculations in the "second stage" of the delayed-acceptance scheme are reordered in such as way that we can obtain a significant speed-up in the MCMC sampling, when the evaluation of the likelihood function is computationally intensive. We consider both simulations studies, and the analysis of real protein folding data. Simulation studies for the stochastic Ricker model and the novel stochastic differential equation model for protein-folding data, show that the speed-up is highly problem dependent. The more involved the computations of the likelihood function are, the higher the acceleration becomes when using our algorithm. Inference results for the standard delayed-acceptance algorithm and our approximated version are similar, indicating that our approximated algorithm can return reliable Bayesian inference. },
  author       = {Wiqvist, Samuel and Picchini, Umberto and Forman, Julie Lyng},
  keyword      = {Bayesian inference,Gaussian process,pseudo marginal MCMC,protein folding,Stochastic differential equation},
  language     = {eng},
  note         = {Working Paper},
  pages        = {55},
  title        = {Accelerating delayed-acceptance Markov chain Monte Carlo algorithms},
  year         = {2018},
}