Testing the Order of Markov Dependence in DNA Sequences

Menéndez, M.; Pardo, Leandro; Pardo, M. C.; Zografos, K.

doi:10.1007/s11009-008-9107-1

Cited by 19 publications

(25 citation statements)

References 9 publications

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Mentioning

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Order By: Relevance

“…The order of the process is then estimated to be the smallest value of r which produces a nonsignificant test statistics [18,19]. Tables II and III for the first row of Table II and subsequently for the second raw to a value 0.392362 × 10 1 , smaller than the χ 2 value of 5.99 at 5% level.…”

Section: Markov Chain Analysismentioning

confidence: 99%

DNA viewed as an out-of-equilibrium structure

Provata

Nicolis

2014

Phys. Rev. E

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The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory and information theory. The use of chi-square tests shows that DNA cannot be described as a low order Markov chain of order up to r = 6. Although detailed balance seems to hold at the level of purine-pyrimidine notation it fails when all four basepairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain we study the exit distances from a specific symbol, the distribution of recurrence distances and the Hurst exponent, all of which show power law tails and long range characteristics. These results suggest that human DNA can be viewed as a non-equilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method we construct a model DNA sequence. This method allows to keep all long range and short range statistical characteristics of the original sequence. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture point-to-point details. *

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Section: Markov Chain Analysismentioning

confidence: 99%

DNA viewed as an out-of-equilibrium structure

Provata

Nicolis

2014

Phys. Rev. E

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“…In Papapetrou and Kugiumtzis (2013), the significance of I C (m) is tested using randomization to form the null distribution ofÎ C (m). The Markov chain order estimation from the scheme of randomization CMI testing for increasing orders m was found to perform consistently well for different scenarios of correlation structure and order of Markov chains, and it was favorably compared to other known order estimation methods, such as the AIC and BIC criteria (Tong, 1975;Katz, 1981;Guttorp, 1995;Csiszár and Shields, 2000), the Peres-Shields estimator (Peres and Shields, 2005), and the likelihood ratio test using a -divergence measure (Menéndez et al, 2001(Menéndez et al, , 2011.…”

Section: Background and Previous Workmentioning

confidence: 91%

Investigating long range correlation in DNA sequences using significance tests of conditional mutual information

Papapetrou¹,

Kugiumtzis²

2014

Computational Biology and Chemistry

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“…We have preferred to use Equation (10) rather than Equations (1) or (6) as the main argument for the divergences because it is much easier to establish a link between Equation (10) and log-linear models: actually both of them deal with (p + 2)-dimensional joint probabilities. This is the reason why the divergence measures we are going to deal with in this paper are very different from those that were used in Menéndez et al [7]. Furthermore, there is a very interesting reason to use log-linear models, the possibility of establishing simultaneously the homogeneity assumption of order p + 1 more rigorously,…”

Section: Statistical Inference Through Log-linear Modelling With Linementioning

confidence: 98%

“…In the book of Billingsley [6] the problem of testing the order of a Markov chain can be seen in a systematic way. In Menéndez et al [7] a family of test statistics is given that contains as a particular case the previous test statistics for studying the order in a given Markov chain. This family of test statistics is based on phi-divergence measures between probability distributions.…”

Section: Introductionmentioning

confidence: 99%

Fitting DNA sequences through log-linear modelling with linear constraints

Martín¹,

Pardo²

2011

Statistics

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For some discrete state series, such as DNA sequences, it can often be postulated that its probabilistic behaviour is given by a Markov chain. For making the decision on whether or not an uncharacterized piece of DNA is part of the coding region of a gene, under the Markovian assumption, there are two statistical tools that are essential to be considered: the hypothesis testing of the order in a Markov chain and the estimators of transition probabilities. In order to improve the traditional statistical procedures for both of them when stationarity assumption can be considered, a new version for understanding the homogeneity hypothesis is proposed so that log-linear modelling is applied for conditional independence jointly with homogeneity restrictions on the expected means of transition counts in the sequence. In addition we can consider a variety of test-statistics and estimators by using φ-divergence measures. As special case of them the well-known likelihood ratio test-statistics and maximum-likelihood estimators are obtained.

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Testing the Order of Markov Dependence in DNA Sequences

Cited by 19 publications

References 9 publications

DNA viewed as an out-of-equilibrium structure

DNA viewed as an out-of-equilibrium structure

Investigating long range correlation in DNA sequences using significance tests of conditional mutual information

Fitting DNA sequences through log-linear modelling with linear constraints

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