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Efficient exact p-value computation for small sample, sparse, and surprising categorical data.

Gill Bejerano1, Nir Friedman, Naftali Tishby

  • 1Center for Biomolecular Science and Engineering, School of Engineering, University of California, Santa Cruz, CA 95064, USA. jill@soe.ucsc.edu

Journal of Computational Biology : a Journal of Computational Molecular Cell Biology
|February 11, 2005
PubMed
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This study introduces a novel branch-and-bound algorithm for fast and exact p-value computation in bioinformatics. The method significantly accelerates hypothesis testing, especially for sparse data and small sample sizes.

Area of Science:

  • Bioinformatics
  • Computational Statistics
  • Statistical Hypothesis Testing

Background:

  • Computing exact p-values is a major computational bottleneck for hypothesis testing in bioinformatics.
  • Existing methods often rely on approximations or computationally intensive exhaustive enumeration.

Purpose of the Study:

  • To develop an efficient exact p-value computation method using a generic branch-and-bound approach.
  • To extend this methodology to the Cressie-Read family of statistics and contingency table tests.

Main Methods:

  • A generic branch-and-bound algorithm is formulated for exact p-value computation.
  • The approach leverages the convexity of statistics for optimization.
  • Explicit procedures are developed for Pearson and likelihood ratio statistics in goodness-of-fit tests.

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Main Results:

  • The new method provides orders of magnitude speed-up compared to exhaustive computation.
  • Increased speed-up is observed with sparser null hypotheses.
  • Computation precision improves with increased speed-up, and time is minimally affected by p-value magnitude.

Conclusions:

  • This computational framework offers a practical and significant improvement for exact hypothesis testing in bioinformatics.
  • The algorithm is particularly advantageous for small samples, sparse distributions, and rare events.
  • It provides a viable alternative to asymptotic approximations and Monte Carlo methods in challenging scenarios.