An Improved Bayesian Information Criterion for Multiple Change-Point Models

In multiple change-point analysis, inferring the number of change points is often achieved by minimizing a selection criterion that trades off data fidelity with complexity. We address the open problem of defining a selection criterion adapted to the context of multiple change-point analysis. Our approach is inspired by the Schwarz seminal formulation of the Bayesian information criterion (BIC): similarly, we introduce priors—here describing the occurrence of change points—and we use the Laplace approximation to derive a closed-form expression of the criterion. Differently from this previous work, we take advantage of the a priori information introduced, instead of asymptotically eliminating the dependence on priors. Results obtained on simulated series show a substantial gain in performance versus recent alternative criteria used in multiple change-point analysis. Results also show that the a priori information introduced in our criterion on the regularity of interevent times is the main driver of this substantial performance gain. Methods are motivated by and demonstrated on a meteorological application involving the homogenization of a temperature series.

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