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The block-Poisson estimator for optimally tuned exact subsampling MCMC
- Publication Year :
- 2016
- Publisher :
- arXiv, 2016.
-
Abstract
- Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators, allowing us to update a single block of subsample indicators in each MCMC iteration so that a desired correlation is achieved between the logs of successive likelihood estimates. This is important since pseudo-marginal MCMC with positively correlated likelihood estimates can use substantially smaller subsamples without adversely affecting the sampling efficiency. The block-Poisson estimator is unbiased but not necessarily positive, so the algorithm runs the MCMC on the absolute value of the likelihood estimator and uses an importance sampling correction to obtain consistent estimates of the posterior mean of any function of the parameters. Our article derives guidelines to select the optimal tuning parameters for our method and shows that it compares very favourably to regular MCMC without subsampling, and to two other recently proposed exact subsampling approaches in the literature.<br />Comment: The main paper is 28 pages. The supplementary material is 28 pages
- Subjects :
- Statistics and Probability
FOS: Computer and information sciences
Computer science
Statistics & Probability
Machine Learning (stat.ML)
Poisson distribution
Control variates
Bayesian inference
01 natural sciences
Statistics - Computation
Methodology (stat.ME)
010104 statistics & probability
symbols.namesake
Statistics - Machine Learning
Block (telecommunications)
0502 economics and business
Discrete Mathematics and Combinatorics
Statistics::Methodology
0101 mathematics
Statistics - Methodology
Computation (stat.CO)
050205 econometrics
05 social sciences
Estimator
Markov chain Monte Carlo
0104 Statistics, 1403 Econometrics
Statistics::Computation
symbols
Statistics, Probability and Uncertainty
Algorithm
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....480a0784550ad5d53ace13a9df6a9cd1
- Full Text :
- https://doi.org/10.48550/arxiv.1603.08232