Scandinavian Working Papers in Economics

Working Paper Series,
Sveriges Riksbank (Central Bank of Sweden)

No 306: SCALABLE MCMC FOR LARGE DATA PROBLEMS USING DATA SUBSAMPLING AND THE DIFFERENCE ESTIMATOR

Matias Quiroz (), Mattias Villani () and Robert Kohn
Additional contact information
Matias Quiroz: Research Department, Central Bank of Sweden, Postal: Sveriges Riksbank, SE-103 37 Stockholm, Sweden
Mattias Villani: Linköping University, Postal: Division of Statistics, and Machine Learning, Department of Computer and Information Science
Robert Kohn: University of New South Wales

Abstract: We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling literature to estimate the log-likelihood accurately using only a small fraction of the data. Our algorithm improves on the O(n) complexity of regular MCMC by operating over local data clusters instead of the full sample when computing the likelihood. The likelihood estimate is used in a Pseudo- marginal framework to sample from a perturbed posterior which is within O(m^-1/2) of the true posterior, where m is the subsample size. The method is applied to a logistic regression model to predict firm bankruptcy for a large data set. We document a significant speed up in comparison to the standard MCMC on the full dataset.

Keywords: Bayesian inference; Markov Chain Monte Carlo; Pseudo-marginal MCMC; estimated likelihood; GLM for large data.

JEL-codes: C11; C13; C15; C55; C83

38 pages, August 1, 2015

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