Markov chain order estimation with conditional mutual information

M. Papapetrou and D. Kugiumtzis

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 7, 1593-1601

Abstract: We introduce the Conditional Mutual Information (CMI) for the estimation of the Markov chain order. For a Markov chain of K symbols, we define CMI of order m, Ic(m), as the mutual information of two variables in the chain being m time steps apart, conditioning on the intermediate variables of the chain. We find approximate analytic significance limits based on the estimation bias of CMI and develop a randomization significance test of Ic(m), where the randomized symbol sequences are formed by random permutation of the components of the original symbol sequence. The significance test is applied for increasing m and the Markov chain order is estimated by the last order for which the null hypothesis is rejected. We present the appropriateness of CMI-testing on Monte Carlo simulations and compare it to the Akaike and Bayesian information criteria, the maximal fluctuation method (Peres–Shields estimator) and a likelihood ratio test for increasing orders using ϕ-divergence. The order criterion of CMI-testing turns out to be superior for orders larger than one, but its effectiveness for large orders depends on data availability. In view of the results from the simulations, we interpret the estimated orders by the CMI-testing and the other criteria on genes and intergenic regions of DNA chains.

Keywords: Order estimation; Markov chains; Conditional mutual information (CMI); Randomization test; DNA (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437112010837
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:7:p:1593-1601

DOI: 10.1016/j.physa.2012.12.017

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().