Scandinavian Working Papers in Economics

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


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: Linköpings University, Postal: Linköping University, 581 83 LINKÖPING
Robert Kohn: Australian School of Business, University of New South Wales

Abstract: The computing time for Markov Chain Monte Carlo (MCMC) algorithms can be prohibitively large for datasets with many observations, especially when the data density for each observation is costly to evaluate. We propose a framework where the likelihood function is estimated from a random subset of the data, resulting in substantially fewer density evaluations. The data subsets are selected using an efficient Probability Proportional-to-Size (PPS) sampling scheme, where the inclusion probability of an observation is proportional to an approximation of its contribution to the log-likelihood function. Three broad classes of approximations are presented. The proposed algorithm is shown to sample from a distribu- tion that is within O(m^-1/2) of the true posterior, where m is the subsample size. Moreover, the constant in the O(m^-1/2) error bound of the likelihood is shown to be small and the approximation error is demonstrated to be negligible even for a small m in our applications. We propose a simple way to adaptively choose the sample size m during the MCMC to optimize sampling efficiency for a fixed computational budget. The method is applied to a bivariate probit model on a data set with half a million observations, and on a Weibull regression model with random effects for discrete-time survival data.

Keywords: Bayesian inference; Markov Chain Monte Carlo; Pseudo-marginal MCMC; Big Data; Probability Proportional-to-Size sampling; Numerical integration.

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

46 pages, March 1, 2015

Full text files

rap_wp297_150330.pdf PDF-file 

Download statistics

Questions (including download problems) about the papers in this series should be directed to Lena Löfgren ()
Report other problems with accessing this service to Sune Karlsson ().

This page generated on 2018-01-23 23:37:35.