Finding Words with Unexpected Frequencies in Deoxyribonucleic Acid Sequences
Bernard Prum, F. Rodolphe, Élisabeth de Turckheim · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1995
SUMMARY Considering a Markov chain model for deoxyribonucleic acid sequences, this paper proposes two asymptotically normal statistics to test whether the frequency of a given word is concordant with the first-order Markov chain model or not. The problem is to choose estimates μ^(W) of the expectation of the frequency Mw of a word W in the observed sequence such that the asymptotic variance of MW−μ^(W) is easily computable. The first estimator is derived from the frequency of W [– 1], which is W with its last letter deleted. The second, following an idea of Cowan, is the conditional expectation Mw given the observed frequencies of all two-letter words. Two examples on phage lambda and phage T7 are shown.