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Open AccessArticle

Consistent Estimation of Partition Markov Models

Department of Statistics, University of Campinas, Rua Sérgio Buarque de Holanda, 651, Campinas, São Paulo 13083-859, Brazil
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Academic Editor: Maxim Raginsky
Entropy 2017, 19(4), 160; https://doi.org/10.3390/e19040160
Received: 1 March 2017 / Revised: 31 March 2017 / Accepted: 4 April 2017 / Published: 6 April 2017
(This article belongs to the Special Issue Information Theory in Machine Learning and Data Science)
The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n goes to infinity, L will be retrieved. We show an application to model internet navigation patterns. View Full-Text
Keywords: Bayesian Information Criterion; distance measure; model selection; statistical inference in Markov processes Bayesian Information Criterion; distance measure; model selection; statistical inference in Markov processes
MDPI and ACS Style

García, J.E.; González-López, V.A. Consistent Estimation of Partition Markov Models. Entropy 2017, 19, 160.

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