Algebraic Statistics for Computational Biology

This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.

L. Pachter (Edited by), B. Sturmfels (Edited by)

9780521857000, Cambridge University Press

Hardback, published 22 August 2005

434 pages, 100 b/w illus. 3 colour illus. 5 tables
26.1 x 18.6 x 2.8 cm, 1.12 kg

'This book is of great interest to research workers, teachers and students in applied statistics, biology, medicine and genetics.' Zentralblatt MATH

The quantitative analysis of biological sequence data is based on methods from statistics coupled with efficient algorithms from computer science. Algebra provides a framework for unifying many of the seemingly disparate techniques used by computational biologists. This book, first published in 2005, offers an introduction to this mathematical framework and describes tools from computational algebra for designing new algorithms for exact, accurate results. These algorithms can be applied to biological problems such as aligning genomes, finding genes and constructing phylogenies. The first part of this book consists of four chapters on the themes of Statistics, Computation, Algebra and Biology, offering speedy, self-contained introductions to the emerging field of algebraic statistics and its applications to genomics. In the second part, the four themes are combined and developed to tackle real problems in computational genomics. As the first book in the exciting and dynamic area, it will be welcomed as a text for self-study or for advanced undergraduate and beginning graduate courses.

Preface
Part I. Introduction to the Four Themes: 1. Statistics L. Pachter and B. Sturmfels
2. Computation L. Pachter and B. Sturmfels
3. Algebra L. Pachter and B. Sturmfels
4. Biology L. Pachter and B. Sturmfels
Part II. Studies on the Four Themes: 5. Parametric inference R. Mihaescu
6. Polytope propagation on graphs M. Joswig
7. Parametric sequence alignment C. Dewey and K. Woods
8. Bounds for optimal sequence alignment S. Elizalde
9. Inference functions S. Elizalde
10. Geometry of Markov chains E. Kuo
11. Equations defining hidden Markov models N. Bray and J. Morton
12. The EM algorithm for hidden Markov models I. B. Hallgrímsdóttir, A. Milowski and J. Yu
13. Homology mapping with Markov random fields A. Caspi
14. Mutagenetic tree models N. Beerenwinkel and M. Drton
15. Catalog of small trees M. Casanellas, L. Garcia and S. Sullivant
16. The strand symmetric model M. Casanellas and S. Sullivant
17. Extending statistical models from trees to splits graphs D. Bryant
18. Small trees and generalized neighbor-joining M. Contois and D. Levy
19. Tree construction using Singular Value Decomposition N. Eriksson
20. Applications of interval methods to phylogenetics R. Sainudiin and R. Yoshida
21. Analysis of point mutations in vertebrate genomes J. Al-Aidroos and S. Snir
22. Ultra-conserved elements in vertebrate genomes M. Drton, N. Eriksson and G. Leung
Index.

Subject Areas: Molecular biology [PSD], Biochemistry [PSB], Probability & statistics [PBT], Algebra [PBF]