Stepwise Signal Extraction via Marginal Likelihood

• Activity Number: 517
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Chao Du*+ and Sam Kou
• Companies: Harvard University and Harvard University
• Keywords: stepwise ; model selection ; bayes factor ; marginal likelihood ; dynamic programming ; changepoint

Abstract

We propose a Bayesian method to analyze the stepwise signal as a special case of the multiple changepoint models with unknown number of changepoints. Our main concern is to estimate the number and the locations of the changepoints in the stepwise signal. We approach this problem from a Bayesian model selection perspective where each possible set of changepoints constitutes a single model. The marginal likelihood and Bayes factor are used as tool of model selection. With the independence assumption between the prior distributions of the parameters associated with the signal segments between successive changepoints, the computational complexity of this approach is at most quadratic in the number of observations using a dynamic programming algorithm. We investigate the choice of the prior, provide an asymptotic justification for our method, and argue for the necessity of using the set of changepoints as basic model unit, rather than the number of changepoints in the Bayesian framework. The performance of our method is demonstrated through detailed comparison with other existing methods and in the applications of well-log data, DNA array CGH data and single molecule data