03-511/711, 15-495/856 Course Notes - Oct. 28, 2010

Gibbs Sampler

A method for discovering ungapped local alignments (Lawrence, et al. '93). See Ewens & Grant, section 6.6 for a straightforward introduction to their algorithm.

Mathematical Framework:

We seek a property of the joint probability distribution of a set of random variables: f(i1, i2, ... ik). For example, these random variables might be the quantities of the ingredients in the cake recipe, or the starting points of a conserved pattern in a set of k sequences. In many cases, calculating the joint probability is hard, but calculating the conditional probability, f(ij | i2, ij-1, ij+1,.. ik) is relatively easy. The Gibbs method simulates the joint distribution by generating an instance of each random variable in turn, conditional on the current values of the remaining k-1 random variables.


Last modified: October 30, 2010.
Maintained by Dannie Durand (durand@cs.cmu.edu) and Annette McLeod.