Statistics Colloquium: Dr. Robert Lund
Title: Bayesian Multiple Breakpoint Detection: Mixing Documented and Undocumented Changepoints
Abstract: This talk presents methods to estimate the number of changepoint time(s) and their locations in time-ordered data sequences when prior information is known about some of the changepoint times. A Bayesian version of a penalized likelihood objective function is developed from minimum description length (MDL) information theory principles. Optimizing the objective function yields estimates of the changepoint number(s) and location time(s). Our MDL penalty depends on where the changepoint(s) lie, but not solely on the total number of changepoints (such as classical AIC and BIC penalties). Specifically, configurations with changepoints that occur relatively closely to one and other are penalized more heavily than sparsely arranged changepoints. The techniques allow for autocorrelation in the observations and mean shifts at each changepoint time. This scenario arises in climate time series where a ``metadata" record exists documenting some, but not necessarily all, of station move times and instrumentation changes. Applications to climate time series are presented throughout.