Two new Markov order estimators

Yuval Peres; Paul Shields

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Two new Markov order estimators

Yuval Peres·Paul Shields

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Abstract

We present two new methods for estimating the order (memory depth) of a finite alphabet Markov chain from observation of a sample path. One method is based on entropy estimation via recurrence times of patterns, and the other relies on a comparison of empirical conditional probabilities. The key to both methods is a qualitative change that occurs when a parameter (a candidate for the order) passes the true order. We also present extensions to order estimation for Markov random fields.

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Yuval Peres, Paul Shields. 2005-06-04. Two new Markov order estimators. https://arxiv.org/abs/math/0506080

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