Reinert, G., Schbath, S.: Compound Poisson Approximations for Occurrences of Multiple Words in Markov Chains, J. Comp. Biol., 5(2), 1998, 223--253. Home/Search Document Not in Database Summary Related Articles Check |
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Three Variations on Word Counting - Régnier, Lifanov, Makeev (1 citation) (Correct)
.... complexity: O(jHj) Then we discuss widely used approximation for the variance V ar(H) E(NH ) When the motif occurrence is a rare event, e.g. when P (H) is small, the Poissonian approximation V E (or V W (E) in the case of palindromic words and double stranded counting) is a very good one [Reinert Schbath, 1998]. However, as this probability increases, the Poissonian approximation becomes less valid and results in a systematic error in Z scores used to assess the statistical signi cance of word preference or avoidance. More precisely, Theorem 1 provides two correcting terms. First, 1 2m)P (H) may not ....
Reinert, G. & Schbath, S. (1998). Compound Poisson Approximation for Occurrences of Multiple Words in Markov Chains. Journal of Computational Biology, 5 (2), 223-253.
Rare Events in Random Strings - Régnier, Denise (Correct)
....known out of the convergence domain, also called the central domain. We study here the tail distribution. First, we consider a single given word, H 1 . In [RS97a, NSF99] a large deviation principle is established, and the rate function is implicitely de ned, but left unsolved, in [RS97a] In [RS98] the authors approximate the exact distribution by the so called compound Poisson distribution, and compute the tail distribution of this approximate distribution. We provide a precise development of the probability out of the convergence domain: we derive a computable formula for the rate ....
....leads to accurate results, with much less computations than exact methods, in the domain where such methods are computable. Experimental evidence is presented in [DRV01] where our results are compared to others ( BFW 00] and RSA tools) Other applications, and a comparison with other methods [RS98, Nue01, RS01] are presented in [R eg02] and will be extended in a forthcoming paper. Maple procedures that implement a part of our results are available on request. An extension to underepresented words is possible, and related results are presented in [Van02] A slight modi cation allows for ....
G. Reinert and S. Schbath. Compound Poisson Approximation for Occurrences of Multiple Words in Markov Chains. Journal of Computational Biology, 5(2):223{ 253, 1998.
Assessing Statistical Significance of.. - Denise.. (2001) (Correct)
....with the exact computation implemented, for the Bernoulli model, in [7] is given in Section 4. It appears that, when the random sequence is large, the formulae above provide an attractive alternative to the exact computation. Morevover, they also hold for the Markov model [3] Another approach [5, 18] is the approximation of the word counting distribution by a compound Poisson distribution with the same mean, e.g. nP(H) in the overlapping counting model. For the compound Poisson distribution de ned in [18] the variance is not asymptotically equal to the variance of the process. As a ....
....computation. Morevover, they also hold for the Markov model [3] Another approach [5, 18] is the approximation of the word counting distribution by a compound Poisson distribution with the same mean, e.g. nP(H) in the overlapping counting model. For the compound Poisson distribution de ned in [18], the variance is not asymptotically equal to the variance of the process. As a consequence, the validity domain is restricted to the domain where the di erence is small. More important, the normalization factor is improper. This implies an error on the rate function I(a) and the neglected term ....
[Article contains additional citation context not shown here]
G. Reinert and S. Schbath. Compound Poisson Approximation for Occurrences of Multiple Words in Markov Chains. Journal of Computational Biology, 5(2):223{ 253,
Assessing the Statistical Significance of.. - Denise, Regnier.. (2001) (Correct)
....with the exact computation implemented, for the Bernoulli model, in [7] is given in Section 4. It appears that, when the random sequence is large, the formulae above provide an attractive alternative to the exact computation. Moreover, they also hold for the Markov model [ 3] Another approach [5,18] is the approximation of the word counting distribution by a compound Poisson distribution with the same mean, e.g. nP(H) in the overlapping counting model. For the compound Poisson distribution defined in [ 18] the variance is not asymptotically equal to the variance of the process. As a ....
....computation. Moreover, they also hold for the Markov model [ 3] Another approach [5,18] is the approximation of the word counting distribution by a compound Poisson distribution with the same mean, e.g. nP(H) in the overlapping counting model. For the compound Poisson distribution defined in [ 18], the variance is not asymptotically equal to the variance of the process. As a consequence, the validity domain is restricted to the domain where the difference is small. More important, the normalization factor is improper. This implies an error on the rate function I(a) and the neglected term ....
[Article contains additional citation context not shown here]
G. Reinert and S. Schbath. Compound Poisson Approximation for Occurrences of Multiple Words in Markov Chains. Journal of Computational Biology, 5(2):223--253,
Regexpcount, a Symbolic Package for Counting Problems on.. - Nicodème (2003) (Correct)
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Reinert, G., Schbath, S.: Compound Poisson Approximations for Occurrences of Multiple Words in Markov Chains, J. Comp. Biol., 5(2), 1998, 223--253.
Rare Events and Conditional Events on Random Strings - Regnier, Denise (2004) (Correct)
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G. Reinert and S. Schbath. Compound Poisson Approximation for Occurrences of Multiple Words in Markov Chains. Journal of Computational Biology, 5(2):223--253, 1998.
Proteome Analysis Based on Motif Statistics - Nicodème, Doerks, Vingron (2002) (Correct)
No context found.
Gesine Reinert and Sophie Schbath. Compound Poisson Approximations for Occurrences of Multiple Words in Markov Chains. J. Comp. Biol., 5(2):223{ 253, 1998.
Fast Approximate Motif Statistics - Nicodème (2001) (Correct)
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Reinert, G., and Schbath, S. Compound Poisson Approximations for Occurrences of Multiple Words in Markov Chains. J. Comp. Biol. 5, 2 (1998), 223-253.
Rare Events and Conditional Events on Random Strings - Regnier, Denise (2004) (Correct)
No context found.
G. Reinert and S. Schbath. Compound Poisson Approximation for Occurrences of Multiple Words in Markov Chains. Journal of Computational Biology, 5(2):223--253, 1998.
Rare Events and Conditional Events on Random Strings - Regnier, Denise (2004) (Correct)
No context found.
G. Reinert and S. Schbath. Compound Poisson Approximation for Occurrences of Multiple Words in Markov Chains. Journal of Computational Biology, 5(2):223--253, 1998.
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