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Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels

Alquier, P., Friel, N., Everitt, R. and Boland, A. (2016) Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels. Statistics and Computing, 26 (1). pp. 29-47. ISSN 1573-1375

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To link to this item DOI: 10.1007/s11222-014-9521-x

Abstract/Summary

Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P. However, there are many situations for which it is impractical or impossible to draw from the transition kernel P. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace P by an approximation Pˆ. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ’close’ the chain given by the transition kernel Pˆ is to the chain given by P . We apply these results to several examples from spatial statistics and network analysis.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics > Applied Statistics
ID Code:37675
Uncontrolled Keywords:Markov chain Monte Carlo Pseudo-marginal Monte Carlo Intractable likelihoods
Publisher:Springer

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