Compound Poisson and Poisson Process Approximations for Occurrences of Multiple Words in Markov Chains
- 1 January 1998
- journal article
- research article
- Published by Mary Ann Liebert Inc in Journal of Computational Biology
- Vol. 5 (2) , 223-253
- https://doi.org/10.1089/cmb.1998.5.223
Abstract
We derive a Poisson process approximation for the occurrences of clumps of multiple words and a compound Poisson process approximation for the number of occurrences of multiple words in a sequence of letters generated by a stationary Markov chain. Using the Chen-Stein method, we provide a bound on the error in the approximations. For rare words, these errors tend to zero as the length of the sequence increases to infinity. Modeling a DNA sequence as a stationary Markov chain, we show as an application that the compound Poisson approximation is efficient for the number of occurrences of rare stem-loop motifs.Keywords
This publication has 9 references indexed in Scilit:
- Compound Poisson approximation of word counts in DNA sequencesESAIM: Probability and Statistics, 1997
- Compound Poisson approximations for word patterns under Markovian hypothesesJournal of Applied Probability, 1995
- Exceptional Motifs in Different Markov Chain Models for a Statistical Analysis of DNA SequencesJournal of Computational Biology, 1995
- Stein's Method for Compound Poisson Approximation: The Local ApproachThe Annals of Applied Probability, 1994
- Compound Poisson Approximation for Nonnegative Random Variables Via Stein's MethodThe Annals of Probability, 1992
- Poisson Approximation and the Chen-Stein MethodStatistical Science, 1990
- Two Moments Suffice for Poisson Approximations: The Chen-Stein MethodThe Annals of Probability, 1989
- Periods in stringsJournal of Combinatorial Theory, Series A, 1981
- Poisson Approximation for Dependent TrialsThe Annals of Probability, 1975