| Function calculateCovariance Calculates the covariance for the number of word occurrences for two words in a sequence of length n, given a background model. calculateCovariance(covariance, word1, word2, backgroundFrequencies, n) calculateCovariance(covariance, word1, word2, bgModel, n) Include Headers seqan/alignment_free.h Parameters
covariance | Variance of the number of occurrences of the word in a sequence of length n given the model Types: double
word1 | Usually a DNA sequence Types: String
word2 | Usually a DNA sequence Types: String
backgroundFrequencies | String of background frequencies representing the model Types: double
bgModel | Markov model Types: MarkovModel
n | Length of the sequence where the occurrences of word are counted Types: integer
Remarks Calculates the covariance for the number of word occurrences for two words in a sequence of length n given a background model (Markov model or Bernoulli model). The covariance is influenced by the property of words to overlap, for example, the words ATAT and TATA have a high covariance since they are likely to overlap. The formula is based on Robin, S., Rodolphe, F., and Schbath, S. (2005). DNA, Words and Models. Cambridge University Press. See Jonathan Goeke et al (to appear) for details on the implementation. Return Values TValue covariance; Covariance of the number of occurrences of the word in a sequence of length n given the model Examples Calculate the covariance for the number of occurrences of ATATAT and TATATA in a sequence of length 10000bp with p(A)=p(T)=0.3 and p(C)=p(G)=0.2. using namespace seqan; double covar = 0.0; int n = 10000; DnaString word1 = "ATATAT"; DnaString word2 = "TATATA"; String<double> model; resize(model, 4); model[0] = 0.3; // p(A) model[1] = 0.2; // p(C) model[2] = 0.2; // p(G) model[3] = 0.3; // p(T) calculateCovariance(covar, word1, word2, model, n); // covar = 4.74 Estimate a Markov model on a set of sequences and calculate the covariance for the number of occurrences of ATATAT and TATATA in a sequence of length 10000bp. using namespace seqan; double covar = 0.0; int n = 10000; DnaString word1 = "ATATAT"; DnaString word2 = "TATATA"; StringSet<DnaString> sequences; appendValue(sequences, "CAGCACTGATTAACAGGAATAAGCAGTTTACTTCTGTCAGAATATTGGGCATATATA" "CTGGGACCCGTGTAATACTCTAATTTAATTAGGTGATCCCTGCGAAGTCTCCA"); MarkovModel<Dna, double> modelMM0(0); // Bernoulli model modelMM0.build(sequences); calculateCovariance(covar, word1, word2, modelMM0, n); // covar = 4.74 MarkovModel<Dna, double> modelMM1(1); // First order Markov model modelMM1.build(sequences); calculateCovariance(covar, word1, word2, modelMM1, n); // covar = 13.1541 See Also alignmentFreeComparison, calculateProbability, MarkovModel, calculateVariance, calculatePeriodicity, countKmers, calculateOverlapIndicator SeqAn - Sequence Analysis Library - www.seqan.de

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