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© 2002

Likelihood, Bayesian, and MCMC Methods in Quantitative Genetics

Book

Part of the Statistics for Biology and Health book series (SBH)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Review of Probability and Distribution Theory

    1. Front Matter
      Pages 1-1
    2. Daniel Sorensen, Daniel Gianola
      Pages 3-75
    3. Daniel Sorensen, Daniel Gianola
      Pages 77-116
  3. Methods of Inference

    1. Front Matter
      Pages 117-117
    2. Daniel Sorensen, Daniel Gianola
      Pages 119-160
    3. Daniel Sorensen, Daniel Gianola
      Pages 161-209
    4. Daniel Sorensen, Daniel Gianola
      Pages 211-285
    5. Daniel Sorensen, Daniel Gianola
      Pages 287-326
    6. Daniel Sorensen, Daniel Gianola
      Pages 327-397
    7. Daniel Sorensen, Daniel Gianola
      Pages 399-442
    8. Daniel Sorensen, Daniel Gianola
      Pages 443-473
  4. Markov Chain Monte Carlo Methods

    1. Front Matter
      Pages 475-475
    2. Daniel Sorensen, Daniel Gianola
      Pages 477-496
    3. Daniel Sorensen, Daniel Gianola
      Pages 497-537
    4. Daniel Sorensen, Daniel Gianola
      Pages 539-560
  5. Applications in Quantitative Genetics

    1. Front Matter
      Pages 561-561
    2. Daniel Sorensen, Daniel Gianola
      Pages 563-604
    3. Daniel Sorensen, Daniel Gianola
      Pages 605-626
    4. Daniel Sorensen, Daniel Gianola
      Pages 627-670

About this book

Introduction

Over the last ten years the introduction of computer intensive statistical methods has opened new horizons concerning the probability models that can be fitted to genetic data, the scale of the problems that can be tackled and the nature of the questions that can be posed. In particular, the application of Bayesian and likelihood methods to statistical genetics has been facilitated enormously by these methods. Techniques generally referred to as Markov chain Monte Carlo (MCMC) have played a major role in this process, stimulating synergies among scientists in different fields, such as mathematicians, probabilists, statisticians, computer scientists and statistical geneticists. Specifically, the MCMC "revolution" has made a deep impact in quantitative genetics. This can be seen, for example, in the vast number of papers dealing with complex hierarchical models and models for detection of genes affecting quantitative or meristic traits in plants, animals and humans that have been published recently.

This book, suitable for numerate biologists and for applied statisticians, provides the foundations of likelihood, Bayesian and MCMC methods in the context of genetic analysis of quantitative traits. Most students in biology and agriculture lack the formal background needed to learn these modern biometrical techniques. Although a number of excellent texts in these areas have become available in recent years, the basic ideas and tools are typically described in a technically demanding style, and have been written by and addressed to professional statisticians. For this reason, considerable more detail is offered than what may be warranted for a more mathematically apt audience.

The book is divided into four parts. Part I gives a review of probability and distribution theory. Parts II and III present methods of inference and MCMC methods. Part IV discusses several models that can be applied in quantitative genetics, primarily from a bayesian perspective. An effort has been made to relate biological to statistical parameters throughout, and examples are used profusely to motivate the developments.

Keywords

Covariance matrix Evolution Excel Multinomial distribution Normal distribution Poisson distribution Probability distribution Radiologieinformationssystem Random variable Variance expectation–maximization algorithm genes genetics linear regression statistics

Authors and affiliations

  1. 1.Department of Animal Breeding and GeneticsDanish Institute of Agricultural SciencesTjeleDenmark
  2. 2.Department of Animal Science, Department of Dairy Science, Department of Biostatistics and Medical InformaticsUniversity of Wisconsin-MadisonMadisonUSA

Bibliographic information

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Reviews

From the reviews:

BIOINFORMATICS

"I found the coverage of material to be excellent: well chosen and well written, and I didn’t spot a single typographical error…It can serve as a resource book for masters-level taught courses, but will be most useful for PhD students and other researchers who need to fill in the gaps in their knowledge, grasp the intuition behind statistical techniques, models, and algorithms, and find pointers to more extensive treatments. Overall, I find that the authors have succeeded admirably in their goals. I highly recommend this excellent book to any researcher seeking a graduate-level introduction to the modern statistical methods applied in quantitative genetics."

"Just one personal sentence as an Introduction: I like the book so much that I have decided to include several parts of it in my own lectures. … it may be understood more easily by students and researchers that lack a strong background in statistics and mathematics. … most examples are nicely explained. … Summing up, I am convinced that this excellent book should be a standard book for researchers and students with a background in genetics who are interested in Bayesian and MCMC methods." (Andreas Ziegler, Metrika, February, 2004)

"Both authors … have made significant contributions to development of statistical methods in quantitative genetics and in particular have been at the forefront of the adoption of MCMC methods for Bayesian analysis, which can be applied to an enormous range of problems … . their coverage of likelihood methods is both extensive and fair. … this is a valuable book, in that it presents so much background essential for the subsequent application and merits a much broader market that it is likely to get." (William G. Hill, Genetical Research, Vol. 81, 2003)

"The coverage of Bayesian theory is extensive, and includes a discussion of information and entropy, and of the notion ‘uninformative’ priors, as well as model assessment and model averaging. … I found the coverage of material to be excellent: well chosen and well written, and I didn’t spot a single typographical error. … the authors have succeeded admirably in their goals. I highly recommend this excellent book to any researcher seeking a graduate-level introduction to the modern statistical methods applied in quantitative genetics." (David Balding, Bioinformatics, July, 2003)

"The book is aimed at students and researchers in agriculture, biology and medicine. … Statisticians will appreciate the attempt to relate biological to statistical parameters. In conclusion the book shows that the authors have a lot of experience with applications of statistics to quantitative genetics. Much more details are given in this book than usual, so it can be considered and recommended for classroom use." (Prof. Dr. W. Urfer, Statistical Papers, Vol. 46 (4), 2005)

" [T]he book is worth owning for anyone interested in applying likelihood or Bayesian models, especially realistic models that may require MCMC for implementation." (Journal of the American Statistical Associaton)