Sampling for Bayesian Computation with Large Datasets

Multilevel models are extremely useful in handling large hierarchical datasets. However, computation can be a challenge, both in storage and CPU time per iteration of Gibbs sampler or other Markov chain Monte Carlo algorithms. We propose a computational strategy based on sampling the data, computing separate posterior distributions based on each sample, and then combining these to get a consensus posterior inference. With hierarchical data structures, we perform cluster sampling into subsets with the same structures as the original data. This reduces the number of parameters as well as sample size for each separate model fit. We illustrate with examples from climate modeling and newspaper marketing.