The mixture model derived to detect haplotype effects on a quantitative trait based on SNP genotype data contains three major parts: (1) the mixture proportions of each distribution, denoted as the relative frequencies of different diplotypes for the same SNP genotype, (2) the mean for each diplotype in the density function, and (3) the residual variance common to all diplotypes.
Four scale mixture models, derived with closed form expressions in [14], are depicted in Table 1, including the Multivariate Gaussian (MG) distribution as a special case.
To facilitate the minimization process, updating rules for parameters of the von Mises-Fisher mixture model are derived.
By incorporating QTL genotypes into the mixture model, we derive an algorithm to estimate these curve parameters for each of the three QTL genotypes.
A homogeneous equilibrium mixture model is subsequently derived for an example flow consisting of bulk solid, bulk fluid, and undrained granular material with compressible constituents.
In our method, the convergence rate of the DAAEM algorithm for mixture model is first derived from Jacobian matrix of the posterior probabilities.
To infer genomic imprinting using such data sets, a multi-hierachical mixture model can be derived to estimate the missing parental genotypes based on observed offspring genotypes.
When data were simulated using a heterotachous mixture model with parameters derived from the empirical data and then analyzed using the same model, BI's support for the incorrect tree increased dramatically, while ML's did not.
The DP mixture model may be derived by considering the limit in Equation (1) (Neal, 1992; Rasmussen, 2000).
Based on the mixture model, we can derive the following probability for a gene X S,i in a given gene set S = { X S,i : i = 1, 2,..., m S }: This probability u S,i can be estimated as by plugging-in the estimated parameters in the PCD model.
