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Scalable Rejection Sampling for Bayesian Hierarchical Models
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 datasets. It can also be used to
compute marginal likelihoods
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