Phys. Rev. E 76, 011106 (2007) [14 pages]Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modelingSee Also: Publisher's Note Received 25 March 2007; published 12 July 2007; publisher error corrected 18 July 2007 Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k, from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes. © 2007 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.76.011106
DOI:
10.1103/PhysRevE.76.011106
PACS:
02.50.Tt, 02.50.Ga, 05.10.Gg
See AlsoPublisher's Note: Christopher C. Strelioff, James P. Crutchfield, and Alfred W. Hübler, Publisher's Note: Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling [Phys. Rev. E 76, 011106 (2007)], Phys. Rev. E 76, 019902 (2007). |
|
About | Terms and Conditions | Subscriptions | Search | Help
Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement. Physical Review®, Physical Review Letters®, Reviews of Modern Physics®, and Physical Review Special Topics® are trademarks of the American Physical Society.