Missing values were imputed via 5-fold multiple imputation involving repeated sampling the empirical multivariate distribution using the Amelia package [ 46] within R statistical programming environment [ 47].
The simulations comprised 20,000 random draws of all model coefficients from multivariate normal distributions using the estimated regression coefficients and their associated variance-covariance matrix.
This paper also, investigates a new and simple method for adaptively refining the covariance matrices of multivariate Gaussian distributions used in the proposed updating strategies.
Possible alternative techniques for fitting the multivariate distributions include using the EM algorithm (Karlis, 2003), a composite likelihood (Jost, Brcich, and Zoubir, 2006) or a symbolic computation approach (Sontag and Zeilberger, 2010).
The statistical model used for multiple imputation is the joint multivariate normal distribution, using Amelia software [ 64, 67- 69].
For each phenotype, we simulated 288 trait values by sampling from a multivariate normal distribution using the mvrnorm function in R with covariance matrix defined by the estimated kinship.
During the first step, for each of the cornerstones the density of the feature vector is approximated by a multivariate normal distribution using data intervals with staging labels only.
Trait values were sampled from a multivariate normal distribution using mvrnorm in R with correlation structure defined by the kinship matrix and the genetic and residual variances were as estimated for HDL.
Because the variances and covariances of the random effects were estimated with uncertainty in the bivariate models, for both of the models, we generated 10,000 realizations of each of the variances and covariances of the random effects from a multivariate normal distribution using the means, variances, and covariances of these estimates calculated by the bivariate random-effects models.
For the MFCC features, the best-fitted candidate was MGD, consistent with the assumption of multivariate Gaussian distribution used in most speech recognition algorithms.
