Maximum Entropy Estimation of Transition Probabilities of Reversible Markov Chains
In this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use one-dimensional classical spin systems to illustrate the theoret...
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| Format: | Article |
| Language: | English |
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MDPI AG
2009-11-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/11/4/867/ |
| _version_ | 1798041646203404288 |
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| author | Erik Van der Straeten |
| author_facet | Erik Van der Straeten |
| author_sort | Erik Van der Straeten |
| collection | DOAJ |
| description | In this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use one-dimensional classical spin systems to illustrate the theoretical ideas. The examples studied in this paper are: the Ising model, the Potts model and the Blume-Emery-Griffiths model. |
| first_indexed | 2024-04-11T22:24:26Z |
| format | Article |
| id | doaj.art-289194162d8448c686487d31637ffdf5 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:24:26Z |
| publishDate | 2009-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-289194162d8448c686487d31637ffdf52022-12-22T03:59:49ZengMDPI AGEntropy1099-43002009-11-0111486788710.3390/e11040867Maximum Entropy Estimation of Transition Probabilities of Reversible Markov ChainsErik Van der StraetenIn this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use one-dimensional classical spin systems to illustrate the theoretical ideas. The examples studied in this paper are: the Ising model, the Potts model and the Blume-Emery-Griffiths model.http://www.mdpi.com/1099-4300/11/4/867/maximum entropy principleMarkov chainparameter estimationstatistical mechanicsspin chain modelsthermodynamics |
| spellingShingle | Erik Van der Straeten Maximum Entropy Estimation of Transition Probabilities of Reversible Markov Chains Entropy maximum entropy principle Markov chain parameter estimation statistical mechanics spin chain models thermodynamics |
| title | Maximum Entropy Estimation of Transition Probabilities of Reversible Markov Chains |
| title_full | Maximum Entropy Estimation of Transition Probabilities of Reversible Markov Chains |
| title_fullStr | Maximum Entropy Estimation of Transition Probabilities of Reversible Markov Chains |
| title_full_unstemmed | Maximum Entropy Estimation of Transition Probabilities of Reversible Markov Chains |
| title_short | Maximum Entropy Estimation of Transition Probabilities of Reversible Markov Chains |
| title_sort | maximum entropy estimation of transition probabilities of reversible markov chains |
| topic | maximum entropy principle Markov chain parameter estimation statistical mechanics spin chain models thermodynamics |
| url | http://www.mdpi.com/1099-4300/11/4/867/ |
| work_keys_str_mv | AT erikvanderstraeten maximumentropyestimationoftransitionprobabilitiesofreversiblemarkovchains |