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Paper No. 08-26

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JAD Aston, JY Peng and DEK Martin

Implied Distributions in Multiple Change Point Problems

Date: November 2008

Abstract: A method for efficiently calculating marginal, conditional and joint distributions for change points defined by general finite state Hidden Markov Models is proposed. The distributions are not subject to any approximation or sampling error once parameters of the model have been estimated. It is shown that, in contrast to sampling methods, very little computation is needed. The method provides probabilities associated with change points within an interval, as well as at specific points.

Keywords: Finite Markov Chain Imbedding, Hidden Markov Models, Change Point Probability, Regime Variability, Run Length Distributions, Generalised Change Points, Waiting Time Distributions.