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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. Daniel Sorensen is Research Leader in Biometrical Genetics, at the Department of Animal Breeding and Genetics in the Danish Institute of Agricultural Sciences. Daniel Gianola is Professor in the Animal Sciences, Biostatistics and Medical Informatics, and Dairy Science Departments of the University of Wisconsin-Madison. Gianola and Sorensen pioneered the introduction of Bayesian and MCMC methods in animal breeding. The authors have published and lectured extensively in applications of statistics to quantitative genetics.
This book provides an introduction to computer-based methods for
the analysis of genomic data. Breakthroughs in molecular and
computational biology have contributed to the emergence of vast
data sets, where millions of genetic markers for each individual
are coupled with medical records, generating an unparalleled
resource for linking human genetic variation to human biology and
disease. Similar developments have taken place in animal and plant
breeding, where genetic marker information is combined with
production traits. An important task for the statistical geneticist
is to adapt, construct and implement models that can extract
information from these large-scale data. An initial step is to
understand the methodology that underlies the probability models
and to learn the modern computer-intensive methods required for
fitting these models. The objective of this book, suitable for
readers who wish to develop analytic skills to perform genomic
research, is to provide guidance to take this first step. This book
is addressed to numerate biologists who typically lack the formal
mathematical background of the professional statistician. For this
reason, considerably more detail in explanations and derivations is
offered. It is written in a concise style and examples are used
profusely. A large proportion of the examples involve programming
with the open-source package R. The R code needed to solve the
exercises is provided. The MarkDown interface allows the students
to implement the code on their own computer, contributing to a
better understanding of the underlying theory. Part I presents
methods of inference based on likelihood and Bayesian methods,
including computational techniques for fitting likelihood and
Bayesian models. Part II discusses prediction for continuous and
binary data using both frequentist and Bayesian approaches. Some of
the models used for prediction are also used for gene discovery.
The challenge is to find promising genes without incurring a large
proportion of false positive results. Therefore, Part II includes a
detour on False Discovery Rate assuming frequentist and Bayesian
perspectives. The last chapter of Part II provides an overview of a
selected number of non-parametric methods. Part III consists of
exercises and their solutions. Daniel Sorensen holds PhD and
DSc degrees from the University of Edinburgh and is an elected
Fellow of the American Statistical Association. He was professor of
Statistical Genetics at Aarhus University where, at present, he is
professor emeritus.
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. Daniel
Sorensen is a Research Professor in Statistical Genetics, at the
Department of Animal Breeding and Genetics in the Danish Institute
of Agricultural Sciences. Daniel Gianola is Professor in the Animal
Sciences, Biostatistics and Medical Informatics, and Dairy Science
Departments of the University of Wisconsin-Madison. Gianola and
Sorensen pioneered the introduction of Bayesian and MCMC methods in
animal breeding. The authors have published and lectured
extensively in applications of statistics to quantitative genetics.
Motivated by Toyota's product development capabilities, Daniel
Sorensen examines the question of how much to invest in pursuing
parallel design alternatives. A real option to switch is modeled
accounting for interproject correlations. Based upon economic
theory, five principles for value-maximizing the product
development process are presented.
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