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Scalable Target Marketing: Distributed Markov Chain Monte Carlo for Bayesian Hierarchical Models

Many problems in marketing and economics require firms to make targeted consumer-specific decisions, but current estimation methods are not designed to scale to the size of modern data sets. In this article, the authors propose a new algorithm to close that gap. They develop a distributed Markov chain Monte Carlo (MCMC) algorithm for estimating Bayesian hierarchical models when the number of consumers is very large and the objects of interest are the consumer-level parameters. The two-stage and embarrassingly parallel algorithm is asymptotically unbiased in the number of consumers, retains the flexibility of a standard MCMC algorithm, and is easy to implement. The authors show that the distributed MCMC algorithm is faster and more efficient than a single-machine algorithm by at least an order of magnitude. They illustrate the approach with simulations with up to 100 million consumers, and with data on 1,088,310 donors to a charitable organization. The algorithm enables an increase of between $1.6 million and $4.6 million in additional donations when applied to a large modern-size data set compared with a typical-size data set.