Scalable MCMC for large data problems using data subsampling and the difference estimator

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Sveriges Riksbank Working Paper Series ; No. 306

Classification and Topics

• Classification: Wirtschaft ; Bayesian Analysis: General ; Estimation: General ; Statistical Simulation Methods: General ; Large Data Sets: Modeling and Analysis ; Survey Methods; Sampling Methods
• Subject: Bayesian inference ; Markov Chain Monte Carlo ; Pseudo-marginal MCMC ; estimated likelihood ; GLM for large data

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Quiroz, Matias ; Villani, Mattias ; Kohn, Robert
• Event: Veröffentlichung
• (who): Sveriges Riksbank
• (where): Stockholm
• (when): 2015

Further information

• Handle: http://hdl.handle.net/10419/129717
• Last update: 10.03.2025, 11:45 AM CET