Elsevier

Applied Mathematical Modelling

Volume 72, August 2019, Pages 202-216
Applied Mathematical Modelling

Multiple change-points detection by empirical Bayesian information criteria and Gibbs sampling induced stochastic search

https://doi.org/10.1016/j.apm.2019.03.012Get rights and content
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Highlights

  • Develop an empirical Bayesian information criterion (emBIC) for change-points detection.

  • Develop a Gibbs sampler induced stochastic search algorithm to find the minimiser of emBIC with probability 1.

  • Develop a 3-step change-points computing procedure, integrating emBIC, Gibbs sampler and post-selection calibration.

Abstract

Uncovering hidden change-points in an observed signal sequence is challenging both mathematically and computationally. We tackle this by developing an innovative methodology based on Markov chain Monte Carlo and statistical information theory. It consists of an empirical Bayesian information criterion (emBIC) to assess the fitness and virtue of candidate configurations of change-points, and a stochastic search algorithm induced from Gibbs sampling to find the optimal change-points configuration. Our emBIC is derived by treating the unknown change-point locations as latent data rather than parameters as is in traditional BIC, resulting in significant improvement over the latter which is known to mostly over-detect change-points. The use of the Gibbs sampler induced search enables one to quickly find the optimal change-points configuration with high probability and without going through computationally infeasible enumeration. We also integrate the Gibbs sampler induced search with a current BIC-based change-points sequential testing method, significantly improving the method’s performance and computing feasibility. We further develop two comprehensive 3-step computing procedures to implement the proposed methodology for practical use. Finally, simulation studies and real examples analyzing business and genetic data are presented to illustrate and assess the procedures.

Keywords

Change-points
Model selection
Bayesian information criteria
Gibbs sampler

MSC

60J22
62C12
65C40

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