Trend Filtering with Adaptive Bayesian Changepoint Analysis for Generalized Data

Oregon Convention Center 

Model development for sequential non-Gaussian data such as counts characterized by small counts and non-stationarities is essential for broader applicability and appropriate inference in the scientific community. Specifically, we introduce global-local shrinkage priors into a Bayesian dynamic generalized linear model to adaptively estimate both changepoints and a smooth trend for non-Gaussian time series. We utilize a parsimonious state-space approach to identify a dynamic signal with local parameters to track smoothness of the local mean at each time-step. This setup provides a flexible framework to detect unspecified changepoints in complex series, such as those with large interruptions in local trends. We detail the extension of our approach to time-varying parameter estimation within dynamic Negative Binomial regression analysis to identify structural breaks. Finally, we illustrate our algorithm with empirical examples in social sciences.