Leo L. Duan, James E. Johndrow, David B. Dunson.
Year: 2018, Volume: 19, Issue: 64, Pages: 1−34
There has been considerable interest in making Bayesian inference more scalable. In big data settings, most of the focus has been on reducing the computing time per iteration rather than reducing the number of iterations needed in Markov chain Monte Carlo (MCMC). This article considers data augmentation MCMC (DA-MCMC), a widely used technique. DA-MCMC samples tend to become highly autocorrelated in large samples, due to a mis-calibration problem in which conditional posterior distributions given augmented data are too concentrated. This makes it necessary to collect very long MCMC paths to obtain acceptably low MC error. To combat this inefficiency, we propose a family of calibrated data augmentation algorithms, which appropriately adjust the variance of conditional posterior distributions. A Metropolis-Hastings step is used to eliminate bias in the stationary distribution of the resulting sampler. Compared to existing alternatives, this approach can dramatically reduce MC error by reducing autocorrelation and increasing the effective number of DA-MCMC samples per unit of computing time. The approach is simple and applicable to a broad variety of existing data augmentation algorithms. We focus on three popular generalized linear models: probit, logistic and Poisson log-linear. Dramatic gains in computational efficiency are shown in applications.