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Likelihood, Bayesian, and MCMC methods in quantitative genetics. (English) Zbl 1013.62105

Statistics for Biology and Health. New York, NY: Springer. xviii, 740 p. (2002).
The aim of this book is to give the key ideas underlying likelihood and Bayesian inference in statistical genetics, with particular emphasis on Markov chain Monte Carlo (MCMC) methods, so that they are accessible to numerate biologists. Derivations are given in great detail, and the examples used are generally from quantitative genetics, including animal breeding, and are fully worked out. The book is organised into four parts as follows.
Part I gives a review of probability and distribution theory, while Part II introduces methods of statistical inference. Part III gives the background to MCMC, and detailed discussion of MCMC procedures, including the Metropolis-Hastings algorithm, the Gibbs sampler and reversible jump MCMC, and finally overviews methods for analysing MCMC output including convergence issues and sensitivity analysis. The final Part presents some of the models that currently are being used in quantitative genetics.
The treatment is mainly Bayesian and the models are implemented via MCMC. They include mixed models for single- and multiple-trait analyses, analyses involving ordered categorical traits based on Wright’s threshold model, models for analysis of longitudinal data, segregation analysis and models for the detection of quantitative trait loci.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62F15 Bayesian inference
62F10 Point estimation
92D10 Genetics and epigenetics
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