Parametric Resampling Methods for Retrospective Changepoint Analysis

Changepoint analysis is a useful tool in environmental statistics in that it provides a methodology for threshold detection and modeling processes subject to periodic changes in the underlying model due to anthropogenic effects or natural phenomena. Several applications of changepoint analysis are investigated here. The use of inappropriate changepoint detection methods is first discussed and the need for a simple, flexible, correct method is established and such a method is proposed for the mean-shift model. Data from the Everglades, Florida, USA is used to showcase the methodology in a real-world setting. An extension to the case of time-series data represented via transition matrices is presented as a result of joint work with Matt Williams (Department of Statistics, Virginia Tech) and rainfall data from Kenya, Africa is presented as a case-study. Finally the multivariate changepoint problem is addressed by a two-stage approach beginning with dimension reduction via principal component analysis (PCA). After the dimension reduction step the location of the changepoint in principal component space is estimated and assuming at most one change in a mean-shift setting, all possible sub-models are investigated.