Dynamic Programming Algorithms for Two Statistical Problems in Computational Biology
We present dynamic programming algorithms for two exact statistical tests that frequently arise in computational biology. The first test concerns the decision whether an observed sequence stems from a given profile (also known as position specific score matrix or position weight matrix), or from an assumed background distribution. We show that the common assumption that the log-odds score has a Gaussian distribution is false for many short profiles, such as transcription factor binding sites or splice sites. We present an efficient implementation of a non-parametric method (first mentioned by Staden) to compute the exact score distribution. The second test concerns the decision whether observed category counts stem from a specified Multinomial distribution. A branch-and-bound method for computing exact p-values for this test was presented by Bejerano at a recent RECOMB conference. Our contribution is a dynamic programming approach to compute the entire distribution of the test statistic, allowing not only the computation of exact p-values for all values of the test statistic simultaneously, but also of the power function of the test. As one of several applications, we introduce p-value based sequence logos, which provide a more meaningful visual description of probabilistic sequences than conventional sequence logos do.
KeywordsTranscription Factor Binding Site Dynamic Program Algorithm Score Distribution Multinomial Distribution Background Distribution
Unable to display preview. Download preview PDF.
- 6.Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in C, 2nd edn. Cambridge University Press, Cambridge (1993)Google Scholar
- 7.Rahmann, S., Müller, T., Vingron, M.: On the power and quality of profiles with applications to transcription factor binding site detection. Unpublished Manuscript (2003)Google Scholar
- 10.Staden, R.: Methods for calculating the probabilities of finding patterns in sequences. CABIOS 5, 89–96 (1989)Google Scholar