A Probabilistic Model for Simultaneous Changepoints in Multiple Data Sequences

• Activity Number: 685
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Zhou Fan* and Lester Mackey
• Companies: Stanford University and Stanford University
• Keywords: changepoint detection ; Bayesian ; copy number variation ; multivariate

Abstract

The detection of changepoints in time series and sequential data is relevant to many applications. Recent applications have motivated the simultaneous analysis of changepoints in multiple related data sequences, as changes often occur at the same sequential locations in several or many sequences. We introduce a probabilistic model for this setting that treats changepoints as unobserved latent variables, and we develop model-based inferential procedures that determine where and in which sequences changepoints occur. Specifically, we propose a Gibbs sampler to approximate the posterior distribution of changepoints, an algorithm to search for the posterior mode, and an MCEM procedure to estimate unknown prior parameters. In our procedures, we use dynamic programming recursions to jointly sample and maximize over groups of latent changepoint variables. We demonstrate on synthetic data that the sampler reaches equilibrium in few iterations, and the posterior mode estimate is competitive in accuracy with existing methods in the literature. We apply our model to the discovery of DNA copy number variations in cancer cell lines and the analysis of historical price volatility in U.S. stocks.