Department of Statistics

Graduate Group in Biostatistics

University of California, Davis

SUMMER SEMINAR

TUESDAY, July 22^nd, 2008 at 1.30pm, MSB 1143 (Statistics Seminar Room)

Refreshments: 3.00pm, MSB 4110 (Statistics Lounge)

Speaker: John Aston (University of Warwick, UK)

Title: Runs, Patterns and Change-points: An HMM Perspective

Abstract: There is a long literature right back to the 1700s discussing probability distributions associated with runs. However, little is known about the distributions of runs and patterns when either noisy observations are made of the process or the patterns occur in an underlying (hidden) process which gives rise to a different observable process, as in the case of an Hidden Markov Model (HMM). Finite state HMMs provide a way to model sequences and time series subject to sudden structural breaks or change points. Exact change point distributions (joint, conditional and margin distributions) in general finite state HMMs, including Markov switching models, will be found by exploiting the duality between the location distributions and the waiting time distributions of runs in the state sequence of an HMM. These distributions can help quantify uncertainty in change point locations and other features of interest in the data series.

The methodology has wide application and examples will be used to motivate its use. These applications include finding the uncertainty in gene locations in bioinfomatics, assessing the uncertainty in recession starts and ends in econometrics and determining emotional changes during psychological experiments performed using fMRI.

Joint work with Michael Jyh-Ying Peng (Academia Sinica) and Donald Martin (NC State)