Andrew Thomas - Colloquium Speaker
In this talk, I will present a novel Bayesian method for multivariate changepoint detection that allows for simultaneous inference on the location of a changepoint and the coefficients of a logistic regression model for distinguishing pre-changepoint data from post-changepoint data. In contrast to many methods for multivariate changepoint detection, the proposed method is applicable to data of mixed type and avoids strict assumptions regarding the distribution of the data and the nature of the change. Additionally, the regression coefficients provide an interpretable description of a change that is potentially complex. For posterior inference, the model admits a simple Gibbs sampling algorithm based on Pólya-gamma data augmentation. I will present conditions under which the proposed method is guaranteed to recover the true underlying changepoint. As a testing ground for our method, we considered the problem of detecting topological changes in time series of images. I will demonstrate that the proposed method, combined with a novel topological feature embedding, performs well on both simulated and real image data. Joint work with Michael Jauch and David S. Matteson.