Page 379 - Applied Probability

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NUMERICAL ANALYSIS PROBABILITY MODELS FOR
FOR STATISTICIANS DNA SEQUENCE EVOLUTION
KENNETH LANGE RICK DURRETT
This book is intended to equip students to craft their Given a collection of DNA sequences, what
own software and to understand the advantages and underlying forces are responsible for the observed
disadvantages of different numerical methods. patterns of variability? The author approaches this
Issues of numerical stability, accurate approxi- question by introducing and analyzing a number
mation, computational complexity, and mathe- of probability models: the Wright-Fisher model,
matical modeling share the limelight in a broad yet the coalescent, the infinite alleles model, and the
rigorous overview of those parts of numerical infinite sites model. He discusses the complica-
analysis relevant to statisticians. Although the tions that come from nonconstant population
bulk of the book covers traditional topics from lin- size, recombination, population subdivision, and
ear algebra, optimization theory, numerical inte- three forms of natural selection: directional selec-
gration, and Fourier analysis, several chapters tion, balancing selection, and background selec-
highlight recent statistical developments such as tion. These theoretical results set the stage for the
wavelets, the bootstrap, hidden Markov chains, and investigation of various statistical tests to detect
Markov chain Monte Carlo methods. departures from “neutral evolution.” The final
chapter studies the evolution of whole genomes
1999/371 PAGES/HARDCOVER/ISBN 0-387-94979-8
STATISTICS AND COMPUTING by chromosomal inversions, reciprocal translo-
cations, and genome duplication.
MATHEMATICAL AND 2002/300 PP./HARDCOVER/ISBN 0-387-95435-X
STATISTICAL METHODS PROBABLILTY AND ITS APPLICATIONS
FOR GENETIC ANALYSIS
Second Edition
To Order or for Information:
KENNETH LANGE
This book enables students in the mathematical In the Americas: CALL: 1-800-SPRINGER or FAX: (201)
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testing of epidemiological hypotheses, molecular
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evolution, and DNA sequence analysis. This sec-
ond edition expands the original edition by over
100 pages and includes new material on DNA
sequence analysis, diffusion processes, binding
domain identification, and QTL mapping and fac- 123
tor analysis.
2002/384 PAGES/HARDCOVER/ISBN 0-387-95389-2 www.springer-ny.com
STATISTICS FOR BIOLOGY AND HEALTH