Scalable Rejection Sampling for Bayesian Hierarchical Models
Marketing Science · 2016 · Volume 35 · Issue 3
Abstract
Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from a large number of units. We develop a new method to sample from posterior distributions of Bayesian models, without using MCMC. Samples are independent, so they can be collected in parallel, and we do not need to be concerned with issues like chain convergence and autocorrelation. The algorithm is scalable under the weak assumption that individual units are conditionally independent, making it applicable for large data sets. It can also be used to compute marginal likelihoods. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mksc.2014.0901 .
Keywords
parallel Bayesian computation, rejection sampling, big data, multilevel models, marginal likelihood, customer heterogeneity, MCMC, sparse optimization, exploiting sparsity
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