Compound Poisson approximation of word counts in DNA sequences
نویسندگان
چکیده
منابع مشابه
Compound Poisson process approximation
Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications a...
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Using recent results on the occurrence times of a string of symbols in a stochastic process with mixing properties, we present a new method for the search of rare words in biological sequences generally modelled by a Markov chain. We obtain a bound on the error between the distribution of the number of occurrences of a word in a sequence (under a Markov model) and its Poisson approximation. A g...
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In this talk, we give an overview about the diierent approximation results existing on the statistical distribution of word counts in a Markov chain. Results concerning the number of overlapping occurrences, the number of non-overlapping occurrences (renewals) and the declumped count will be presented. Counts of single words but also multiple words and word families are considered. We will see ...
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ژورنال
عنوان ژورنال: ESAIM: Probability and Statistics
سال: 1997
ISSN: 1292-8100,1262-3318
DOI: 10.1051/ps:1997100