Lawrence

Bayesian Inference Algorithms.

Application of these Bayesian concepts to bioinformatics. Both a general formulation and two specific examples are given. The results of the application of these methods bioploymer sequence data sets are given in order to help fix students understanding. Access to the software that implements these methods for use after the tutorial is also provided.

Sequence alignment without gap penalties or selection of a scoring matrix is just one product of a full Bayesian approach to bioinformatics. Other products include the following: 1) exact significance measures; 2) explicit elucidation of variation in conservation at different points in the sequences; 3) the exact probability of the best alignment as a measure of its merit. Furthermore, since essentially any of the dynamic programming algorithms used in bioinformatics can be converted into a Bayesian equivalent similar advantages are accessible for a broad range of bioinformatics problems. A two part tutorial describing these concepts and their algorithmic implementation will be presented. Since we assume no background in Bayesian statistics, the first half day gives an overview of Bayesian statistics and associated probability theory. A spread sheet based mini-laboratory is included to help fix key concepts. On the second half day, we describe a general paradigm for the formulation of existing dynamic programming algorithms as stochastic models appropriate to Bayesian statistics, and for their conversion into Bayesian inference algorithms. A simple concrete example, sequence segmentation via composition, is used through out to help fix these general concepts. Application of these concepts to pairwise alignment via the Bayes aligner will also be presented (Zhu J, Liu JS, and Lawrence CE. ISMB, 5:358, 1997 & Bioinformatics 2/98). We also show how these methods may be generalized to multiple sequences via the Gibbs sampler (Liu JS, and Lawrence, CE. Proc. Amer. Statist. Assoc., Statistical Computing Section, 21:1-8, 1995)