Gibbs sampling methods in genetics
W.R. Gilks, S. Richardson, David Spiegelhalter · 1995
As described in Section 23.2.1, the marginal (population) distribution of a major disease gene depends only on q, the frequency of the high risk allele A. The probability that a parent with genotype G = aa, aA or AA transmits allele A to an offspring is TG = 0, ½or 1, respectively. Thus, for a major gene model, the factors of (23.2) have the form { P( G; lq) for founders P(GilG1, .. •, G;-1; q, r) = P(G IG G . ) f f&s; d &s; i M;, F;, T or nonroun ers (23.3) P(z;lz1, ... ,z;-i)= N(2MtF,½) for founders for nonfounders &s; (23.4) (where N(a, b) denotes a normal distribution with mean a and variance b). Hence, in a pure polygenic model there are no parameters in 0 to be estimated.