Corpus ID: 88514161

Efficiency of delayed-acceptance random walk Metropolis algorithms

@article{Sherlock2015EfficiencyOD,
  title={Efficiency of delayed-acceptance random walk Metropolis algorithms},
  author={Chris Sherlock and Alexandre Hoang Thiery and Andrew Golightly},
  journal={arXiv: Statistics Theory},
  year={2015}
}
Delayed-acceptance Metropolis-Hastings and delayed-acceptance pseudo-marginal Metropolis-Hastings algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased stochastic approximation thereof, but a computationally cheap deterministic approximation is available. An initial accept-reject stage uses the cheap approximation for computing the Metropolis-Hastings ratio; proposals which are accepted at this stage are then subjected to a further accept… Expand

Figures and Tables from this paper

Adaptive, Delayed-Acceptance MCMC for Targets With Expensive Likelihoods
TLDR
The resulting adaptive, delayed-acceptance [pseudo-marginal] Metropolis–Hastings algorithm is justified both theoretically and empirically and applied to a discretely observed Markov jump process characterizing predator–prey interactions and an ODE system describing the dynamics of an autoregulatory gene network. Expand
Variance bounding of delayed-acceptance kernels
A delayed-acceptance version of a Metropolis--Hastings algorithm can be useful for Bayesian inference when it is computationally expensive to calculate the true posterior, but a computationally cheapExpand
Speeding Up MCMC by Delayed Acceptance and Data Subsampling
The complexity of Markov Chain Monte Carlo (MCMC) algorithms arises from the requirement of a likelihood evaluation for the full data set in each iteration. Payne and Mallick (2014) propose to speedExpand
Speeding up MCMC by Delayed Acceptance and Data Subsampling
TLDR
A more precise likelihood estimator is proposed that incorporates auxiliary information about the full data likelihood while only operating on a sparse set of the data and is provably within O(m− 2) of the true posterior. Expand
Delayed Acceptance ABC-SMC
TLDR
This article employs delayed acceptance Markov chain Monte Carlo within an ABC sequential Monte Carlo sampler to use the cheap simulator to rule out parts of the parameter space that are not worth exploring, and shows that this approach can be used quite automatically, with few tuning parameters. Expand
Importance sampling type correction of Markov chain Monte Carlo and exact approximations
We use an importance sampling (IS) type correction of approximate Markov chain Monte Carlo (MCMC) output in order to provide consistent estimators. The IS approach, based on unbiased estimators,Expand
Accelerating sequential Monte Carlo with surrogate likelihoods
TLDR
Overall, this work develops a novel algorithm for computationally efficient SMC with expensive likelihood functions that utilise the history of the sampler to adaptively tune the surrogate likelihood to yield better approximations of the expensive likelihood. Expand
Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo
TLDR
This work considers importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution and shows that the IS type approach can provide substantial gains relative to an analogous DA scheme, and is often competitive even without parallelisation. Expand
Importance sampling correction versus standard averages of reversible MCMCs in terms of the asymptotic variance
Abstract We establish an ordering criterion for the asymptotic variances of two consistent Markov chain Monte Carlo (MCMC) estimators: an importance sampling (IS) estimator, based on an approximateExpand
Efficient Sequential Monte Carlo Algorithms for Integrated Population Models
TLDR
An efficient particle Markov chain Monte Carlo algorithm is proposed to estimate demographic parameters without a need for linear or Gaussian approximations and this algorithm is incorporated into a sequential Monte Carlo sampler to perform model comparison. Expand
...
1
2
...

References

SHOWING 1-10 OF 90 REFERENCES
Adaptive, Delayed-Acceptance MCMC for Targets With Expensive Likelihoods
TLDR
The resulting adaptive, delayed-acceptance [pseudo-marginal] Metropolis–Hastings algorithm is justified both theoretically and empirically and applied to a discretely observed Markov jump process characterizing predator–prey interactions and an ODE system describing the dynamics of an autoregulatory gene network. Expand
Variance bounding of delayed-acceptance kernels
A delayed-acceptance version of a Metropolis--Hastings algorithm can be useful for Bayesian inference when it is computationally expensive to calculate the true posterior, but a computationally cheapExpand
On the efficiency of pseudo-marginal random walk Metropolis algorithms
We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computedExpand
Accelerating Metropolis-Hastings algorithms by Delayed Acceptance
TLDR
A useful generalisation of the Delayed Acceptance approach, devised to reduce the computational costs of Metropolis-Hastings algorithms by a simple and universal divide-and-conquer strategy, is offered. Expand
Delayed acceptance particle MCMC for exact inference in stochastic kinetic models
TLDR
The method is illustrated by considering inference for parameters governing a Lotka–Volterra system, a model of gene expression and a simple epidemic process to avoid expensive calculations for proposals that are likely to be rejected. Expand
Delayed Acceptance ABC-SMC
TLDR
This article employs delayed acceptance Markov chain Monte Carlo within an ABC sequential Monte Carlo sampler to use the cheap simulator to rule out parts of the parameter space that are not worth exploring, and shows that this approach can be used quite automatically, with few tuning parameters. Expand
Optimal scaling of the random walk Metropolis on elliptically symmetric unimodal targets
Scaling of proposals for Metropolis algorithms is an important practical problem in MCMC implementation. Criteria for scaling based on empirical acceptance rates of algorithms have been found to workExpand
Optimal Scaling of the Random Walk Metropolis: General Criteria for the 0.234 Acceptance Rule
TLDR
Criteria for scaling based on empirical acceptance rates of algorithms have been found to work consistently well across a broad range of problems and are shown to hold for targets arising from a p-th order Markov process, and spherically symmetric targets where the log-density is a polynomial function of the radius. Expand
Efficient MCMC Schemes for Computationally Expensive Posterior Distributions
TLDR
This work considers combining the original method with tempering schemes in order to deal with multimodal posterior distributions and replaces the original target posterior distribution with the Gaussian process approximation, which requires less computation to evaluate. Expand
Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo
TLDR
This work considers importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution and shows that the IS type approach can provide substantial gains relative to an analogous DA scheme, and is often competitive even without parallelisation. Expand
...
1
2
3
4
5
...