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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 539-569

\vspace{3pc} \normalsize \centerline{\large\bf A SIMPLE BAYESIAN
APPROACH TO} \vspace{2pt} \centerline{\large\bf MULTIPLE
CHANGE-POINTS} \vspace{.25cm}
\author{Tze Leung Lai and Haipeng Xing}
\vspace{.4cm} \centerline{\it Stanford University and SUNY at Stony
Brook} \vspace{.55cm} \sz09
\begin{quotation}
\noindent {\it Abstract:} After a brief review of previous
frequentist and Bayesian approaches to multiple change-points, we
describe a Bayesian model for multiple parameter changes in a
multiparameter exponential family. This model has attractive
statistical and computational properties and yields explicit
recursive formulas for the Bayes estimates of the piecewise constant
parameters. Efficient estimators of the hyperparameters of the
Bayesian model for the parameter jumps can be used in conjunction,
yielding empirical Bayes estimates. The empirical Bayes approach is
also applied to solve long-standing frequentist problems such as
significance testing of the null hypothesis of no change-points
versus multiple change-point alternatives, and inference on the
number and locations of change-points that partition the unknown
parameter sequence into segments of equal values. Simulation studies
of performance and an illustrative application to the British coal
mine data are also given. Extensions from the exponential family to
general parametric families and from independent observations to
genearlized linear time series models are then provided.
\par
\vspace{9pt} \noindent {\it Key words and phrases:} Empirical Bayes,
exponential families, generalized linear autoregressive models,
multiple change-points, segmentation.
\par
\end{quotation}

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