By Richard Durbin, Sean R. Eddy, Anders Krogh, Graeme Mitchison
Probablistic versions have gotten more and more very important in interpreting the massive quantity of information being produced via large-scale DNA-sequencing efforts reminiscent of the Human Genome venture. for instance, hidden Markov versions are used for reading organic sequences, linguistic-grammar-based probabilistic types for settling on RNA secondary constitution, and probabilistic evolutionary types for inferring phylogenies of sequences from assorted organisms. This ebook provides a unified, updated and self-contained account, with a Bayesian slant, of such tools, and extra in most cases to probabilistic equipment of series research. Written by way of an interdisciplinary group of authors, it's obtainable to molecular biologists, computing device scientists, and mathematicians without formal wisdom of the opposite fields, and whilst provides the cutting-edge during this new and significant box.
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Additional resources for Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids
A simple estimate of the number of start points of local matches is the product of the lengths of the sequences, nm. If all matches were constant length and all start points gave independent matches, this would result in a requirement to compare the best score S with log(nm). However, these assumptions are both clearly wrong (for instance, match segments at consecutive points along a diagonal are not independent), with the consequence that a further small correction factor should be added to S, dependent only on the scoring function s, but not on n and m.
Because of this, the same type of significance test can be used for any search method that looks for the best score from a large set of equivalent possibilities. Indeed, for best local match scores from the local alignment algorithm, the best score between two (significantly long) sequences will itself be distributed according to the extreme value distribution, because in this case we are effectively comparing the outcomes of O(nm) distinct random starts within the single matrix. For local ungapped alignments, Karlin & Altschul  derived the appropriate EVD distribution analytically, using results given more fully in Dembo & Karlin .
A particular example of where the prior odds ratio becomes important is when we are looking at a large number of different alignments for a possible significant match. This is the typical situation when searching a database. It is clear that if we have a fixed prior odds ratio, then even if all the database sequences are unrelated, as the number of sequences we try to match increases, the probability of one of the matches looking significant by chance will also increase. In fact, given a fixed prior odds ratio, the expected number of (falsely) significant observations will increase linearly.
Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids by Richard Durbin, Sean R. Eddy, Anders Krogh, Graeme Mitchison