Projects per year

### Abstract

We study convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (Andrieu and Roberts [Ann. Statist. 37 (2009) 697- 725]).We find that the asymptotic variance of the pseudo-marginal 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 pseudo-marginal 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 Metropolis-Hastings or a random-walk Metropolis targeting a super-exponential 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 |
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Pages (from-to) | 1030-1077 |

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
- Pseudo-marginal algorithm

## Fingerprint Dive into the research topics of 'Convergence properties of pseudo-marginal 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

## Cite this

*Annals of Applied Probability*,

*25*(2), 1030-1077. https://doi.org/10.1214/14-AAP1022