Titlebook: Mathematical and Statistical Methods for Genetic Analysis; Kenneth Lange Textbook 2002Latest edition Springer Science+Business Media New Y

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Genetic Identity Coefficients,ric autosomal locus and depend only on the relevant pedigree connecting two relatives and not on any phenotypes observed in the pedigree. In Chapter 6 we will investigate the applications of identity coefficients. Readers desiring motivation for the combinatorial problems attacked here may want to glance at Chapter 6 first.

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Descent Graph Methods, productive alternatives use elementary graph theory. The Lander-Green-Kruglyak algorithm alluded to in Chapter 7 exploits gene flow graphs and works well on small pedigrees. For large pedigrees, it is helpful to combine the graph theory perspective with stochastic methods of numerical integration [12, 23, 24, 32, 39, 40, 42].

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Radiation Hybrid Mapping,ophisticated and successful versions raise many fascinating statistical problems. We will first discuss the mathematically simpler case of haploid radiation hybrids. Once this case is thoroughly digested, we will turn to the mathematically subtler case of polyploid radiation hybrids.

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Ingrained

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Counting Methods and the EM Algorithm,dels, geneticists by and large rely on maximum likelihood estimators rather than on competing estimators derived from minimax, invariance, robustness, or Bayesian principles. A host of methods exists for numerically computing maximum likelihood estimates. Some of the most appealing involve simple co

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,Newton’s Method and Scoring,owever, the trade-offs of programming ease, numerical stability, and speed of convergence are complex, and statistical geneticists should be fluent in a variety of numerical optimization techniques for finding maximum likelihood estimates. Outside the realm of maximum likelihood, Bayesian procedures

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Hypothesis Testing and Categorical Data,ests or likelihood ratio tests based on large sample theory. Although one could easily dismiss this conservatism as undue reverence for Karl Pearson and R. A. Fisher, it is grounded in the humble reality of geneticists’ inability to describe precise alternative hypotheses and to impose convincing pr

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Genetic Identity Coefficients,reeding of a single individual and the degree of relatedness of a pair of relatives. Since the degree of inbreeding of a single individual can be summarized by the relationship between his or her parents, we will focus on identity coefficients for relative pairs. These coefficients pertain to a gene

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