Table 1.

Accuracy of MCMC Parameter Estimates^[Note]

Scenario	Mi (DispersionCompared withNormal Theory)a	λi (DispersionCompared withNormal Theory)a	Residual of pAj and pBj (Dispersion Compared with Normal Theory)b
Null model (scenario 1) (see also fig. 5)	20.0% (2.1-fold)	6.0 (2.0-fold)	−.02 (2.1-fold)
Mi varies between parents (scenario 2)	19.9% (1.9-fold)	5.6 (10.7-fold)	−.01 (2.0-fold)
λi varies between parents (scenario 3)	19.6% (2.3-fold)	5.8 (2.3-fold)	−.02 (2.0-fold)

Note.— We assessed how well the MCMC estimates unknown parameters by performing simulations of 1,000 individuals without disease studied at 2,147 markers from the map described by Smith et al. (2004 [in this issue]). The simulations assume that the samples have percentages of European ancestry with distributions of M_i∼20%±12% and λ_i∼6±2 generations. The frequencies of the markers are based on the West African and European American frequencies from the Smith et al. (2004 [in this issue]) map. The data for simulations of admixture conforming fully to our model are presented in the first row (and pictorially in fig. 5). The means of both M_i and λ_i are within 7% of their true values even in the presence of large deviations from the model, and the allele frequency estimates are essentially unaffected by deviations from the model. The dispersions (measuring the spread of the residuals around the mean) are generally more than twice the values expected from normal theory. This indicates that the MCMC is overconfident about its parameter estimates. However, this does not appear to increase the values of disease association statistics, and, hence, it would not be expected to lead to false positives (table 2).

^aValues for M_i and λ_i are averaged over 1,000 individuals (if estimates are unbiased, they should be M_i=20% and λ_i=6 generations).

^bValues for p^A_j and p^B_j are the mean residuals (the difference between the true and estimated value, divided by the estimated SE) out of 2,147 × 2 frequency estimates; should be ∼0 if unbiased.