Parallelized Langevin Hastings Sampling

• Activity Number: 123
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Matthew M. Tibbits*+ and Murali Haran and John Liechty and Benjamin Shaby
• Companies: Penn State University and Penn State University and Penn State University and Statistical and Applied Mathematical Sciences Institute
• Keywords: Langevin Hastings ; Spatial GLMs ; Dynamic Epidemic Modelling ; Markov chain Monte Carlo ; Parallel MCMC ; Automated Tuning Procedure

Abstract

Langevin Hastings (LH) algorithms are often utilized for multivariate distributions with strong dependence among the variables. In such cases, standard MCMC algorithms (e.g. random walk Metropolis-Hastings) typically result in slow mixing Markov chains. Using local information, the gradient and Hessian, the efficiency of the LH algorithm can be significantly improved. Because the gradient and Hessian often do not exist in closed form, we rely on numerical approximations, which can greatly slow down the modified LH algorithm. We demonstrate that parallel processing can mitigate the impact of the expensive approximations whilst preserving their benefit to the LH algorithm. Furthermore, while Markov chain Monte Carlo methods typically require the user to specify tuning parameters which vary for each model and every dataset considered, we construct an algorithm that automatically identifies reasonable values for LH based on a short initial run. We investigate the performance of the modified, parallelized LH algorithm within the context of two challenging examples: inference for a spatial generalized linear model, and a model for dynamic epidemic propagation across a social network.