TITLE: BIC Applied to Model Selection of a Large Number of Change-points

SPEAKER: Professor David Siegmund

ABSTRACT:

In a previous paper (Biometrics, 2006, pp. 22-32) we derived a Bayes Information Criterion (BIC) for determining the number of change-points in a sequence of independent
observations when the number $m$ of change-points is assumed to remain bounded as the number of observations increases. Here we generalize that result to include multiple aligned sequences with intervals of simultaneous change that occur in a fraction of the sequences and a total number of of change-points $m$ that can increase with the sample size; and we include in the criterion terms that increase at rate $m$. Stochastic terms that enter into the new criterion involve integrals and maxima of two-sided Brownian motion
with negative drift. Examples involve segmenting aligned DNA sequences according to copy number variations that occur at the same position in a fraction of the sequences.

This is joint research with N. Zhang.