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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.

Bayesian Change Point Detection with Spike-and-Slab Priors