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Large sample asymptotics of the pseudo-marginal method
- Source :
- Pitt, M K, Deligiannidis, G, Doucet, A & SCHMON, S 2020, ' Large Sample Asymptotics of the Pseudo-Marginal Method ', BIOMETRIKA, vol. 2020, asaa044 . https://doi.org/10.1093/biomet/asaa044
- Publication Year :
- 2020
- Publisher :
- Oxford University Press, 2020.
-
Abstract
- The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density. Practically, one has to trade-off the computational resources used to obtain this estimator against the asymptotic variances of the ergodic averages obtained by the pseudo-marginal algorithm. Recent works optimizing this trade-off rely on some strong assumptions which can cast doubts over their practical relevance. In particular, they all assume that the distribution of the difference between the log-density and its estimate is independent of the parameter value at which it is evaluated. Under regularity conditions we show here that, as the number of data points tends to infinity, a space-rescaled version of the pseudo-marginal chain converges weakly towards another pseudo-marginal chain for which this assumption indeed holds. A study of this limiting chain allows us to provide parameter dimension-dependent guidelines on how to optimally scale a normal random walk proposal and the number of Monte Carlo samples for the pseudo-marginal method in the large-sample regime. This complements and validates currently available results.<br />Comment: 76 pages, 3 figures
- Subjects :
- Statistics and Probability
FOS: Computer and information sciences
Weak convergence
Applied Mathematics
General Mathematics
05 social sciences
Monte Carlo method
Estimator
Random walk
Statistics - Computation
01 natural sciences
Agricultural and Biological Sciences (miscellaneous)
010104 statistics & probability
Random measure
Metropolis–Hastings algorithm
0502 economics and business
Applied mathematics
Probability distribution
Ergodic theory
0101 mathematics
Statistics, Probability and Uncertainty
General Agricultural and Biological Sciences
Computation (stat.CO)
050205 econometrics
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Pitt, M K, Deligiannidis, G, Doucet, A & SCHMON, S 2020, ' Large Sample Asymptotics of the Pseudo-Marginal Method ', BIOMETRIKA, vol. 2020, asaa044 . https://doi.org/10.1093/biomet/asaa044
- Accession number :
- edsair.doi.dedup.....c56dcef49e38d9aae54548d6f55dd393