Probabilistic and statistical properties of words: An overview

@article{citeulike:2770271, abstract = {In the following, an overview is given on statistical and probabilistic properties of words, as occurring in the analysis of biological sequences. Counts of occurrence, counts of clumps, and renewal counts are distinguished, and exact distributions as well as normal approximations, Poisson process approximations, and compound Poisson approximations are derived. Here, a sequence is modelled as a stationary ergodic Markov chain; a test for determining the appropriate order of the Markov chain is described. The convergence results take the error made by estimating the Markovian transition probabilities into account. The main tools involved are moment generating functions, martingales, Stein's method, and the Chen-Stein method. Similar results are given for occurrences of multiple patterns, and, as an example, the problem of unique recoverability of a sequence from SBH chip data is discussed. Special emphasis lies on disentangling the complicated dependence structure between word occurrences, due to self-overlap as well as due to overlap between words. The results can be used to derive approximate, and conservative, confidence intervals for tests.}, address = {King's Coll. and Stat. Laboratory, King's Parade, Cambridge CB2 1ST, United Kingdom}, author = {Reinert, G. and Schbath, S. and Waterman, M. S. }, citeulike-article-id = {2770271}, doi = {http://dx.doi.org/10.1089/10665270050081360}, journal = {Journal of Computational Biology}, keywords = {words}, number = {1-2}, pages = {1--46}, posted-at = {2008-05-08 09:58:09}, priority = {5}, title = {Probabilistic and statistical properties of words: An overview}, url = {http://dx.doi.org/10.1089/10665270050081360}, volume = {7}, year = {2000} }

TY - JOUR ID - citeulike:2770271 L3 - citeulike-article-id:2770271 TI - Probabilistic and statistical properties of words: An overview JF - Journal of Computational Biology VL - 7 IS - 1-2 SP - 1 EP - 46 AD - King's Coll. and Stat. Laboratory, King's Parade, Cambridge CB2 1ST, United Kingdom N2 - In the following, an overview is given on statistical and probabilistic properties of words, as occurring in the analysis of biological sequences. Counts of occurrence, counts of clumps, and renewal counts are distinguished, and exact distributions as well as normal approximations, Poisson process approximations, and compound Poisson approximations are derived. Here, a sequence is modelled as a stationary ergodic Markov chain; a test for determining the appropriate order of the Markov chain is described. The convergence results take the error made by estimating the Markovian transition probabilities into account. The main tools involved are moment generating functions, martingales, Stein's method, and the Chen-Stein method. Similar results are given for occurrences of multiple patterns, and, as an example, the problem of unique recoverability of a sequence from SBH chip data is discussed. Special emphasis lies on disentangling the complicated dependence structure between word occurrences, due to self-overlap as well as due to overlap between words. The results can be used to derive approximate, and conservative, confidence intervals for tests. KW - words AU - Reinert, G AU - Schbath, S AU - Waterman, MS PY - 2000/// UR - http://dx.doi.org/10.1089/10665270050081360 ER -