Bayesian Change Point Detection with Spike-and-Slab Priors

Abstract

We study the use of spike-and-slab priors for consistent estimation of the number of change points and their locations. Leveraging recent results in the variable selection literature, we show that an estimator based on spike-and-slab priors achieves optimal localization rate in the multiple offline change point detection problem. Based on this estimator, we propose a Bayesian change point detection method, which is one of the fastest Bayesian methodologies. We demonstrate through empirical work the good performance of our approach vis-a-vis some state-of-the-art benchmarks. Interestingly, despite having a Gaussian noise assumption, our approach is more robust to misspecification of the error terms than the competing methods in numerical experiments. Supplementary materials for this article are available online.

KEYWORDS:

• Approximate inference
• Optimality
• Robust
• Shrinkage

Acknowledgments

We thank an associate editor and two anonymous reviewers for constructive comments.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

Computing resources were provided by Stanford University research computing center (Sherlock cluster) and Pompeu Fabra Marvin cluster. Oscar Padilla acknowledges support from NSF DMS-2015489.