## Statistics Colloquium: Dr. Robert Lund

#### Clemson University

**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.