Rare Events and Conditional Events on Random Strings
Some strings -the texts- are assumed to be randomly generated, according to a probability model that is either a Bernoulli model or a Markov model. A rare event is the over or under-representation of a word or a set of words. The aim of this paper is twofold. First, a single word is given. One...
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Discrete Mathematics & Theoretical Computer Science
2004-12-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/186 |
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doaj-337652cdbfd24a93bab2348bd84fb5502020-11-24T23:47:18ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1462-72641365-80502004-12-0162Rare Events and Conditional Events on Random StringsMireille RégnierAlain DeniseSome strings -the texts- are assumed to be randomly generated, according to a probability model that is either a Bernoulli model or a Markov model. A rare event is the over or under-representation of a word or a set of words. The aim of this paper is twofold. First, a single word is given. One studies the tail distribution of the number of its occurrences. Sharp large deviation estimates are derived. Second, one assumes that a given word is overrepresented. The distribution of a second word is studied; formulae for the expectation and the variance are derived. In both cases, the formulae are accurate and actually computable. These results have applications in computational biology, where a genome is viewed as a text. http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/186 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Mireille Régnier Alain Denise |
| spellingShingle |
Mireille Régnier Alain Denise Rare Events and Conditional Events on Random Strings Discrete Mathematics & Theoretical Computer Science |
| author_facet |
Mireille Régnier Alain Denise |
| author_sort |
Mireille Régnier |
| title |
Rare Events and Conditional Events on Random Strings |
| title_short |
Rare Events and Conditional Events on Random Strings |
| title_full |
Rare Events and Conditional Events on Random Strings |
| title_fullStr |
Rare Events and Conditional Events on Random Strings |
| title_full_unstemmed |
Rare Events and Conditional Events on Random Strings |
| title_sort |
rare events and conditional events on random strings |
| publisher |
Discrete Mathematics & Theoretical Computer Science |
| series |
Discrete Mathematics & Theoretical Computer Science |
| issn |
1462-7264 1365-8050 |
| publishDate |
2004-12-01 |
| description |
Some strings -the texts- are assumed to be randomly generated, according to a probability model that is either a Bernoulli model or a Markov model. A rare event is the over or under-representation of a word or a set of words. The aim of this paper is twofold. First, a single word is given. One studies the tail distribution of the number of its occurrences. Sharp large deviation estimates are derived. Second, one assumes that a given word is overrepresented. The distribution of a second word is studied; formulae for the expectation and the variance are derived. In both cases, the formulae are accurate and actually computable. These results have applications in computational biology, where a genome is viewed as a text. |
| url |
http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/186 |
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AT mireilleregnier rareeventsandconditionaleventsonrandomstrings AT alaindenise rareeventsandconditionaleventsonrandomstrings |
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