Lecture 7 Statistical Models January 27 , 1998 Lecturer

In previous lectures we have discussed using the general expectation maximization algorithm to find an optimal weight matrix that indicated the probability for finding a given symbol at a given location in a motif. The weight matrix model has two main limitations in its ability to describe a family of related sequences, protein or otherwise. First of all, the weight matrix only allows comparison to sequences of fixed length, a length given by the size of the weight matrix. Second, the weight matrix is not able to model the dependence of one position in the sequence on the identity of its neighbors, or other locations within the sequence. Effectively each position in the sequence is compared to the matrix independently of the rest of the sequence. In this lecture we use the same general algorithm, but this time we let it operate on a more powerful model which gives more flexibility in describing the structure and variability of a family of motifs. This model is called a Hidden Markov Model [2].