We develop a theory to measure the variance and covariance of probability distributions defined on nodes graph, which takes into account distance between nodes. Our approach generalizes usual (co)variance setting weighted graphs retains many its intuitive desired properties. Interestingly, we find that number famous concepts in graph network science can be reinterpreted this as variances covari...

The skull is a developmentally complex and highly integrated structure. Integration, which is manifested as covariance among structures, enables the skull and associated soft tissues to maintain function both across ontogeny within individuals and across the ranges of size and shape variation among individuals. Integration also contributes to evolvability by structuring the phenotypic expressio...

Variance components of the covariance function coefficients in a random regression test-day model were estimated by Legendre polynomials up to a fifth order for first-parity records of Dutch dairy cows using Gibbs sampling. Two Legendre polynomials of equal order were used to model the random part of the lactation curve, one for the genetic component and one for permanent environment. Test-day ...

We consider the problem of testing of a Kronecker product structured variance covariance matrix against the unstructured variance covariance matrix in the context of multivariate repeated measures data. A likelihood ratio test statistic is developed for this purpose. However, the test statistic for this test cannot be expressed in a closed form. An algorithm, is suggested for the maximum likeli...

Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and variance-covariance identity matrix. In this paper, we propose to release random effects to non-normal distributions and discuss how to model the mean and covariance structures in GLMMs s...