Application of Lifting Transform To Detect Change Points
Arunendu Chatterjee
Mathematics, University of Wisconsin River Falls, River Falls, WI, United States

We use wavelets within a Bayesian framework to identifychanges in the form of shifts in data collected over time in thepresence of noise and missing observations. We modify and extend anexisting Bayesian change point detection procedure due to Ogden andLynch (1999) which uses the discrete wavelet transform. Our maincontribution is to investigate the usefulness of the procedure forreal data sets, and to modify it by using one of the more recentlifting transform to identify change points, specifically using anadaptive lifting procedure due to Nunes et al. (2006). Our researchwas motivated by a problem encountered in the analysis of waterpressure data. To that effect, we first conducted a simulation studybased on which, we provide recommendations for the choice oflifting-based wavelet coefficients to be used in the change pointdetection procedure in the context of different jump sizes, noisevariances and missing observations. We present results for otherreal data problems from the change point literature where theexistence and timing of change points are known.

Keywords: Bayesian method; Wavelets; Lifting

Biography: Arunendu Chatterjee after reaching his Ph. D. from University of Wyoming in Fall 2009, is currently holding the position of an Assistant Professor at Department of Mathematics, University of Wisconsin, River Falls. His primary area of expertiseis to apply Bayesian modeling technique to detect change points in time series data. He is also applying his Bayesian modeling skillsin different inter-disciplinary subjects such as Chemistry, Glaciology and Communicative disorder. He published a journal article on application of non parametric statistics in Biostatistics.