Consistent Estimation of Partition Markov Models
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 p...
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| Format: | Article |
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MDPI AG
2017-04-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/19/4/160 |
| _version_ | 1828392470110535680 |
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| author | Jesús E. García Verónica A. González-López |
| author_facet | Jesús E. García Verónica A. González-López |
| author_sort | Jesús E. García |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T07:20:18Z |
| format | Article |
| id | doaj.art-7dc7c56c96c74190827e4cbfa0d82b5f |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-12-10T07:20:18Z |
| publishDate | 2017-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-7dc7c56c96c74190827e4cbfa0d82b5f2022-12-22T01:57:49ZengMDPI AGEntropy1099-43002017-04-0119416010.3390/e19040160e19040160Consistent Estimation of Partition Markov ModelsJesús E. García0Verónica A. González-López1Department of Statistics, University of Campinas, Rua Sérgio Buarque de Holanda, 651, Campinas, São Paulo 13083-859, BrazilDepartment of Statistics, University of Campinas, Rua Sérgio Buarque de Holanda, 651, Campinas, São Paulo 13083-859, BrazilThe 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.http://www.mdpi.com/1099-4300/19/4/160Bayesian Information Criteriondistance measuremodel selectionstatistical inference in Markov processes |
| spellingShingle | Jesús E. García Verónica A. González-López Consistent Estimation of Partition Markov Models Entropy Bayesian Information Criterion distance measure model selection statistical inference in Markov processes |
| title | Consistent Estimation of Partition Markov Models |
| title_full | Consistent Estimation of Partition Markov Models |
| title_fullStr | Consistent Estimation of Partition Markov Models |
| title_full_unstemmed | Consistent Estimation of Partition Markov Models |
| title_short | Consistent Estimation of Partition Markov Models |
| title_sort | consistent estimation of partition markov models |
| topic | Bayesian Information Criterion distance measure model selection statistical inference in Markov processes |
| url | http://www.mdpi.com/1099-4300/19/4/160 |
| work_keys_str_mv | AT jesusegarcia consistentestimationofpartitionmarkovmodels AT veronicaagonzalezlopez consistentestimationofpartitionmarkovmodels |