Importance sampling correction versus standard averages of reversible MCMCs in terms of the asymptotic variance

Franks, Jordan; Vihola, Matti

doi:10.1016/j.spa.2020.05.006

Cited by 9 publications

(5 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although the theoretical understanding of delayedacceptance methods is still limited, several results are available. [55] compares the ergodicity properties of a delayed-acceptance algorithm with those of the parent MH algorithm, while [28] compares the asymptotic variance of the ergodic average from a delayed-acceptance algorithm with the variance of an importance-sampling estimator which takes as its proposal a sample from an MCMC algorithm targeting a surrogate. Historically, insights into the performance and tuning of MCMC algorithms have been obtained by examining the limiting behaviour of a rescaled version of the Markov chain as the dimension of the statespace increases to infinity [6,8,44,45,46,57,62,63].…”

Section: Introductionmentioning

confidence: 99%

Efficiency of delayed-acceptance random walk Metropolis algorithms

2021

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

Efficiency of delayed-acceptance random walk Metropolis algorithms

2021

View full text Add to dashboard Cite

“…Likewise, in case of , the result holds because we may regard as an augmented version of (e.g. Franks and Vihola 2020 ). We conclude that where the integral defines a probability measure independent of .…”

Section: Appendixmentioning

confidence: 89%

Conditional particle filters with diffuse initial distributions

Karppinen

Vihola

2021

Stat Comput

Self Cite

View full text Add to dashboard Cite

Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random walk type transitions which are reversible with respect to a uniform initial distribution (on some domain), and autoregressive kernels for Gaussian initial distributions. We propose to use online adaptations within the methods. In the case of random walk transition, our adaptations use the estimated covariance and acceptance rate adaptation, and we detail their theoretical validity. We tested our methods with a linear Gaussian random walk model, a stochastic volatility model, and a stochastic epidemic compartment model with time-varying transmission rate. The experimental findings demonstrate that our method works reliably with little user specification and can be substantially better mixing than a direct particle Gibbs algorithm that treats initial states as parameters.

show abstract

“…For example, it could be used as the cheap approximate likelihood within a delayed-acceptance MCMC algorithm (e.g. Sherlock et al, 2017 and or importance sampling scheme (Franks and Vihola, 2017). Alternatively, we might bridge our approximate posterior with the true posterior using sequential Monte Carlo.…”

Section: Neuroscience Example Modelmentioning

confidence: 99%

Ensemble MCMC: Accelerating Pseudo-Marginal MCMC for State Space Models using the Ensemble Kalman Filter

et al. 2022

View full text Add to dashboard Cite

Particle Markov chain Monte Carlo (pMCMC) is now a popular method for performing Bayesian statistical inference on challenging state space models (SSMs) with unknown static parameters. It uses a particle filter (PF) at each iteration of an MCMC algorithm to unbiasedly estimate the likelihood for a given static parameter value. However, pMCMC can be computationally intensive when a large number of particles in the PF is required, such as when the data are highly informative, the model is misspecified and/or the time series is long. In this paper we exploit the ensemble Kalman filter (EnKF) developed in the data assimilation literature to speed up pMCMC. We replace the unbiased PF likelihood with the biased EnKF likelihood estimate within MCMC to sample over the space of the static parameter. On a wide class of different non-linear SSM models, we demonstrate that our extended ensemble MCMC (eMCMC) methods can significantly reduce the computational cost whilst maintaining reasonable accuracy. We also propose several extensions of the vanilla eMCMC algorithm to further improve computational efficiency. Computer code to implement our methods on all the examples can be downloaded from https://github.com/cdrovandi/ Ensemble-MCMC.

show abstract

Importance sampling correction versus standard averages of reversible MCMCs in terms of the asymptotic variance

Cited by 9 publications

References 49 publications

Efficiency of delayed-acceptance random walk Metropolis algorithms

Efficiency of delayed-acceptance random walk Metropolis algorithms

Conditional particle filters with diffuse initial distributions

Ensemble MCMC: Accelerating Pseudo-Marginal MCMC for State Space Models using the Ensemble Kalman Filter

Contact Info

Product

Resources

About