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Activity Number: 234 - Bayesian Conditional Models and Updates
Type: Contributed
Date/Time: Monday, July 31, 2017 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #322970
Title: Calibrated Data Augmentation for Scalable Markov Chain Monte Carlo
Author(s): Leo Duan* and James Johndrow and David Dunson
Companies: Johns Hopkins University and Stanford University and Duke University
Keywords: Bayesian probit ; Bayesian logit ; Big n ; Data Augmentation ; Maximal Correlation ; Polya-Gamma
Abstract:

Data augmentation is a common technique for building tuning-free Markov chain Monte Carlo algorithms. Although these algorithms are very popular, autocorrelations are often high in large samples, leading to poor computational efficiency. This phenomenon has been attributed to a discrepancy between Gibbs step sizes and the rate of posterior concentration. In this article, we propose a family of calibrated data augmentation algorithms, which adjust for this discrepancy by inflating Gibbs step sizes while adjusting for bias. A Metropolis-Hastings step is included to account for the slight discrepancy between the stationary distribution of the resulting sampler and the exact posterior distribution. The approach is applicable to a broad variety of existing data augmentation algorithms, and we focus on three popular models: probit, logistic and Poisson log-linear. Theoretical support is provided and dramatic gains are shown in applications.


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