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We present a Bayesian method for multivariate changepoint detection thatallows for simultaneous inference on the location of a changepoint and thecoefficients of a logistic regression model for distinguishing pre-changepointdata from post-changepoint data. In contrast to many methods for multivariatechangepoint detection, the proposed method is applicable to data of mixed typeand avoids strict assumptions regarding the distribution of the data and thenature of the change. The regression coefficients provide an interpretabledescription of a potentially complex change. For posterior inference, the modeladmits a simple Gibbs sampling algorithm based on P\'olya-gamma dataaugmentation. We establish conditions under which the proposed method isguaranteed to recover the true underlying changepoint. As a testing ground forour method, we consider the problem of detecting topological changes in timeseries of images. We demonstrate that the proposed method, combined with anovel topological feature embedding, performs well on both simulated and realimage data.

Bayesian changepoint detection via logistic regression and the topological analysis of image series