Projects per year
Abstract
We study convergence properties of pseudomarginal Markov chain Monte Carlo algorithms (Andrieu and Roberts [Ann. Statist. 37 (2009) 697 725]).We find that the asymptotic variance of the pseudomarginal algorithm is always at least as large as that of the marginal algorithm.We show that if the marginal chain admits a (right) spectral gap and the weights (normalised estimates of the target density) are uniformly bounded, then the pseudomarginal chain has a spectral gap. In many cases, a similar result holds for the absolute spectral gap, which is equivalent to geometric ergodicity. We consider also unbounded weight distributions and recover polynomial convergence rates in more specific cases, when the marginal algorithm is uniformly ergodic or an independent MetropolisHastings or a randomwalk Metropolis targeting a superexponential density with regular contours. Our results on geometric and polynomial convergence rates imply central limit theorems. We also prove that under general conditions, the asymptotic variance of the pseudomarginal algorithm converges to the asymptotic variance of the marginal algorithm if the accuracy of the estimators is increased.
Original language  English 

Pages (fromto)  10301077 
Number of pages  48 
Journal  Annals of Applied Probability 
Volume  25 
Issue number  2 
DOIs  
Publication status  Published  1 Apr 2015 
Keywords
 Asymptotic variance
 Geometric ergodicity
 Markov chain Monte Carlo
 Polynomial ergodicity
 Pseudomarginal algorithm
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Dive into the research topics of 'Convergence properties of pseudomarginal markov chain monte carlo algorithms'. Together they form a unique fingerprint.Projects
 2 Finished

Bayesian Inference for Big Data with Stochastic Gradient Markov Chain Monte Carlo
31/08/13 → 31/08/16
Project: Research

Intractable Likelihood: New Challenges from Modern Applications (ILike)
1/01/13 → 30/06/18
Project: Research
Profiles

Professor Christophe Andrieu
 Statistical Science
 Probability, Analysis and Dynamics
 School of Mathematics  Professor in Statistics
 Statistics
Person: Academic , Member