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E.A. Thompson 455TABLE 39.2The changing pattern of genetic data (1970–2010).Date Marker Type Data Structure Trait Type1970 Blood types Nuclear families Mendelian1980 RFLPs Large pedigrees Simple traits1990 STRs Small pedigrees Quantitative traits(Microsatellites)2000 SNPs and Case/Control Complex traitsmRNA expression data (“unrelated”)2010 RNAseq and Relatives in ComplexSequence data populations quantitative traitsevant structure became the Markov dependence of inheritance (S) of DNAat successive marker (M) or hypthesized trait (T) locations across a chromosome,as shown in Figure 39.1(b). As before the population model providesprobabilities of the allelic types (A) of founders (F ), at trait (T ) or marker(M) loci. At a locus, the observable data (Y )isdeterminedbythefounderallelic types (A) and the inheritance (S) at that locus, possibly through apenetrance model in the case of trait loci.39.4 The 1990s: MCMC and complex stochastic systemsThe earlier methods (Figure 39.1(a)) are computationally exponential in thenumber of genetic loci analyzed jointly, the hidden Markov model (HMM)methods (Figure 39.1(b)) are exponential in the number of meioses in a pedigree.Neither could address large numbers of loci, observed on large numbersof related individuals. However, the same conditional independence structuresthat make possible the computation of linkage likelihoods for few markers orfor small pedigrees, lend themselves to Markov chain Monte Carlo (MCMC).Genetic examples, as well as other scientific areas, gave impetus to the hugeburst of MCMC in the early 1990s. However, unlike other areas, where MCMCwas seen as a tool for Bayesian computation (Gelfand and Smith, 1990; Besagand Green, 1993) in statistical genetics the focus on likelihood inferenceled rather to Monte Carlo likelihood (Penttinen, 1984; Geyer and Thompson,1992).The discreteness and the constraints of genetic models provided challengesfor MCMC algorithms. Earlier methods (Lange and Sobel, 1991) usedthe genotypes of individuals as latent variables (Figure 39.1(a)) and encoun-