# Scalable Rejection Sampling for Bayesian Hierarchical Models 

Michael Braun Cox School of Business Southern Methodist University Dallas, TX 75275 braunm@smu.edu 

November 2, 2014 

Paul Damien McCombs School of Business University of Texas at Austin Austin, TX 78712 paul.damien@mccombs.utexas.edu 

## Forthcoming in Marketing Science Special Issue on Big Data: Integrating Marketing, Statistics and Computer Science 

## Abstract 

Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogene- ity 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 mod- els, 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 in- dependent, making it applicable for large datasets. It can also be used to compute marginal likelihoods. 

