Closed-Form Estimation of Multiple Change-Point Models

Abstract

Identifying discontinuities (or change-points ) in otherwise stationary time series is a powerful analytic tool. This paper outlines a general strategy for identifying an unknown number of change-points using elementary principles of Bayesian statistics. Using a strategy of binary partitioning by marginal likelihood , a time series is recursively subdivided on the basis of whether adding divisions (and thus increasing model complexity) yields a justified improvement in the marginal model likelihood. When this approach is combined with the use of conjugate priors, it yields the Conjugate Partitioned Recursion (CPR) algorithm, which identifies change-points without computationally intensive numerical integration. Using the CPR algorithm, methods are described for specifying change-point models drawn from a host of familiar distributions, both discrete (binomial, geometric, Poisson) and continuous (exponential, Gaussian, uniform, and multiple linear regression), as well as multivariate distribution (multinomial, multivariate normal, and multivariate linear regression). Methods by which the CPR algorithm could be extended or modified are discussed, and several detailed applications to data published in psychology and biomedical engineering are described.

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