Commentary: Revisiting Scalable Targeted Marketing with Distributed Markov Chain Monte Carlo

Abstract

Bumbaca, Misra, and Rossi (2020) propose a parallelizable algorithm for estimating a large number of customer-level parameters in a Bayesian hierarchical model. However, the algorithm follows from a mathematical error in the derivation of the target posterior density, which calls into question the theoretical support for the algorithm sampling from the specified model. Adapting the algorithm to be consistent with the corrected math nullifies the claimed benefits in scalability and efficiency. Notwithstanding that error, unbiasedness requires the number of customers to be asymptotic per computational node, which is more restrictive than being asymptotic in the size of the dataset as a whole. The more the algorithm is parallelized, the greater the bias. Potential adopters should be aware that the algorithm does not sample from the exact posterior distribution, and that its ability to take advantage of distributed computing infrastructure is limited.

Editor's Note

This article identifies a mathematical error in the derivation of the algorithm published in Bumbaca, Misra and Rossi (2020). This paper underwent a regular review process at JMR. The editorial team at JMR agreed that the error warranted clarification and helped the author develop a concise paper explaining the issue to JMR readers. A reply from Bumbaca, Misra and Rossi was invited and is published in the same issue.