Compound Poisson approximation of word counts in DNA sequences
ESAIM: PS, 1 (1997) 1-16
Published online: 2002-08-15
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Malliavin calculus for marked binomial processes and applications
Hélène HalconruyElectronic Journal of Probability 27 (none) (2022)
https://doi.org/10.1214/22-EJP892
Cycle counts and affinities in stochastic models of nonequilibrium systems
Patrick Pietzonka, Jules Guioth and Robert L. JackPhysical Review E 104 (6) (2021)
https://doi.org/10.1103/PhysRevE.104.064137
The Shortest Possible Return Time of
$\beta$
-Mixing Processes
Miguel Abadi, Sandro Gallo and Erika Alejandra Rada-MoraIEEE Transactions on Information Theory 64 (7) 4895 (2018)
https://doi.org/10.1109/TIT.2017.2757494
5094 (2016)
https://doi.org/10.1109/IJCNN.2016.7727871
Wavelet Thresholding Estimation in a Poissonian Interactions Model with Application to Genomic Data
Laure SansonnetScandinavian Journal of Statistics 41 (1) 200 (2014)
https://doi.org/10.1111/sjos.12009
Poisson and compound Poisson approximations in conventional and nonconventional setups
Yuri Kifer and Ariel RapaportProbability Theory and Related Fields 160 (3-4) 797 (2014)
https://doi.org/10.1007/s00440-013-0541-9
Approximation for counts of 2-runs in a two state Markov chain
Hui Chen and Mei ZhangActa Mathematica Sinica, English Series 29 (10) 1907 (2013)
https://doi.org/10.1007/s10114-013-1709-z
919 (2012)
https://doi.org/10.1109/BMEI.2012.6513091
Probabilistic Arithmetic Automata and Their Applications
Tobias Marschall, Inke Herms, Hans-Michael Kaltenbach and Sven RahmannIEEE/ACM Transactions on Computational Biology and Bioinformatics 9 (6) 1737 (2012)
https://doi.org/10.1109/TCBB.2012.109
Normal and Compound Poisson Approximations for Pattern Occurrences in NGS Reads
Zhiyuan Zhai, Gesine Reinert, Kai Song, et al.Journal of Computational Biology 19 (6) 839 (2012)
https://doi.org/10.1089/cmb.2012.0029
Extreme Value Methods with Applications to Finance
C&H/CRC Monographs on Statistics & Applied Probability, Extreme Value Methods with Applications to Finance 20114852 351 (2011)https://doi.org/10.1201/b11537-18
Distribution of Clump Statistics for a Collection of Words
Donald E. K. Martin and Deidra A. ColemanJournal of Applied Probability 48 (4) 1049 (2011)
https://doi.org/10.1239/jap/1324046018
Approximation for counts of head runs
Mei ZhangScience China Mathematics 54 (2) 311 (2011)
https://doi.org/10.1007/s11425-010-4104-6
An Evolutionary Distance Based on Maximal Unique Matches
Frédéric Guyon and Alain GuénocheCommunications in Statistics - Theory and Methods 39 (3) 385 (2010)
https://doi.org/10.1080/03610920903140213
The Power of Detecting Enriched Patterns: An HMM Approach
Zhiyuan Zhai, Shih-Yen Ku, Yihui Luan, et al.Journal of Computational Biology 17 (4) 581 (2010)
https://doi.org/10.1089/cmb.2009.0218
Large deviations and full Edgeworth expansions for finite Markov chains with applications to the analysis of genomic sequences
Pierre PudloESAIM: Probability and Statistics 14 435 (2010)
https://doi.org/10.1051/ps/2009008
Scan Statistics
Sophie Schbath and Stéphane RobinScan Statistics 319 (2009)
https://doi.org/10.1007/978-0-8176-4749-0_15
Assessing the Exceptionality of Coloured Motifs in Networks
Sophie Schbath, Vincent Lacroix and Marie-France SagotEURASIP Journal on Bioinformatics and Systems Biology 2009 (1) 616234 (2009)
https://doi.org/10.1186/1687-4153-2009-616234
Moderate Deviations for Word Counts in Biological Sequences
Sarah Behrens and Matthias LöweJournal of Applied Probability 46 (4) 1020 (2009)
https://doi.org/10.1239/jap/1261670686
Assessing the Exceptionality of Coloured Motifs in Networks
Sophie Schbath, Vincent Lacroix and Marie-France SagotEURASIP Journal on Bioinformatics and Systems Biology 2009 1 (2009)
https://doi.org/10.1155/2009/616234
Comparing bacterial genomes from linear orders of patterns
Frédéric Guyon and Alain GuénocheDiscrete Applied Mathematics 156 (8) 1251 (2008)
https://doi.org/10.1016/j.dam.2007.04.030
Two sufficient conditions for Poisson approximations in the ferromagnetic Ising model
David CoupierThe Annals of Applied Probability 18 (4) (2008)
https://doi.org/10.1214/1214/07-AAP487
Cumulative distribution function of a geometric Poisson distribution
Grégory NuelJournal of Statistical Computation and Simulation 78 (3) 385 (2008)
https://doi.org/10.1080/10629360600997371
Assessing the Exceptionality of Network Motifs
F. Picard, J.-J. Daudin, M. Koskas, S. Schbath and S. RobinJournal of Computational Biology 15 (1) 1 (2008)
https://doi.org/10.1089/cmb.2007.0137
Compound Poisson Approximation of the Number of Occurrences of a Position Frequency Matrix (PFM) on Both Strands
Utz J. Pape, Sven Rahmann, Fengzhu Sun and Martin VingronJournal of Computational Biology 15 (6) 547 (2008)
https://doi.org/10.1089/cmb.2007.0084
String Matching and 1d Lattice Gases
Muhittin MunganJournal of Statistical Physics 126 (1) 207 (2007)
https://doi.org/10.1007/s10955-006-9247-z
Waiting times for clumps of patterns and for structured motifs in random sequences
V.T. Stefanov, S. Robin and S. SchbathDiscrete Applied Mathematics 155 (6-7) 868 (2007)
https://doi.org/10.1016/j.dam.2005.07.016
Statistical tests to compare motif count exceptionalities
Stéphane Robin, Sophie Schbath and Vincent VandewalleBMC Bioinformatics 8 (1) (2007)
https://doi.org/10.1186/1471-2105-8-84
Improved compound Poisson approximation for the number of occurrences of any rare word family in a stationary markov chain
Etienne Roquain and Sophie SchbathAdvances in Applied Probability 39 (1) 128 (2007)
https://doi.org/10.1239/aap/1175266472
Exact distribution of word counts in shuffled sequences
Einar Andreas RødlandAdvances in Applied Probability 38 (1) 116 (2006)
https://doi.org/10.1239/aap/1143936143
Pattern statistics on Markov chains and sensitivity to parameter estimation
Grégory NuelAlgorithms for Molecular Biology 1 (1) (2006)
https://doi.org/10.1186/1748-7188-1-17
Nonrandom Clusters of Palindromes in Herpesvirus Genomes
Ming-Ying Leung, Kwok Pui Choi, Aihua Xia and Louis H.Y. ChenJournal of Computational Biology 12 (3) 331 (2005)
https://doi.org/10.1089/cmb.2005.12.331
Checking Homogeneity of Motifs' Distribution in Heterogenous Sequences
Sabrina Ledent and Stéphane RobinJournal of Computational Biology 12 (6) 672 (2005)
https://doi.org/10.1089/cmb.2005.12.672
The Distributions of the Frequency of Occurrence of Nucleotide Subsequences
Chufang WuMethodology and Computing in Applied Probability 7 (3) 325 (2005)
https://doi.org/10.1007/s11009-005-4520-1
A compound Poisson model for word occurrences in DNA sequences
Stephane RobinJournal of the Royal Statistical Society: Series C (Applied Statistics) 51 (4) 437 (2002)
https://doi.org/10.1111/1467-9876.00279
Distributional regimes for the number of k -word matches between two random sequences
Ross A. Lippert, Haiyan Huang and Michael S. WatermanProceedings of the National Academy of Sciences 99 (22) 13980 (2002)
https://doi.org/10.1073/pnas.202468099
Compound Poisson approximation: a user's guide
A. D. Barbour and O. ChryssaphinouThe Annals of Applied Probability 11 (3) (2001)
https://doi.org/10.1214/aoap/1015345355
Numerical Comparison of Several Approximations of the Word Count Distribution in Random Sequences
Stéphane Robin and Sophie SchbathJournal of Computational Biology 8 (4) 349 (2001)
https://doi.org/10.1089/106652701752236179
An Overview on the Distribution of Word Counts in Markov Chains
Sophie SchbathJournal of Computational Biology 7 (1-2) 193 (2000)
https://doi.org/10.1089/10665270050081469
Probability and Statistical Models with Applications
A Barbour, O Chryssaphinou and E VaggelatouProbability and Statistical Models with Applications (2000)
https://doi.org/10.1201/9781420036084.ch3
Probabilistic and Statistical Properties of Words: An Overview
Gesine Reinert, Sophie Schbath and Michael S. WatermanJournal of Computational Biology 7 (1-2) 1 (2000)
https://doi.org/10.1089/10665270050081360
Compound Poisson approximation for counts of rare patterns in Markov chains and extreme sojourns in birth-death chains
Torkel ErhardssonThe Annals of Applied Probability 10 (2) (2000)
https://doi.org/10.1214/aoap/1019487356
Exact distribution of word occurrences in a random sequence of letters
S. Robin and J. J. DaudinJournal of Applied Probability 36 (1) 179 (1999)
https://doi.org/10.1239/jap/1032374240
Probability Towards 2000
Louis H. Y. ChenLecture Notes in Statistics, Probability Towards 2000 128 97 (1998)
https://doi.org/10.1007/978-1-4612-2224-8_6
On the Distribution of K-tuple Matches for Sequence Homology: A Constant Time Exact Calculation of the Variance
GARY BENSON and XIAOPING SUJournal of Computational Biology 5 (1) 87 (1998)
https://doi.org/10.1089/cmb.1998.5.87
Compound Poisson and Poisson Process Approximations for Occurrences of Multiple Words in Markov Chains
GESINE REINERT and SOPHIE SCHBATHJournal of Computational Biology 5 (2) 223 (1998)
https://doi.org/10.1089/cmb.1998.5.223
Explicit distributional results in pattern formation
A. G. Pakes and V. T. StefanovThe Annals of Applied Probability 7 (3) (1997)
https://doi.org/10.1214/aoap/1034801248