Statistical associations between phenotypic traits often result from shared developmental processes and include both covariation between the trait values and more complex associations between higher moments of the joint distribution of traits. In this article, an analytical technique for calculating the covariance between traits is presented on the basis of (1). the distribution of underlying g...

Recent research has pointed to the ubiquity and abundance of between-generation epigenetic inheritance. This research has implications for assessing disease risk and the responses to ecological stresses and also for understanding evolutionary dynamics. An important step toward a general evaluation of these implications is the identification and estimation of the amount of heritable, epigenetic ...

Given a collection of single-market covariance matrix forecasts for different markets, we describe how to embed them into a global forecast of total risk. We do this by starting with any global covariance matrix forecast that contains information about cross-market correlations, and revising it to agree with the pre-specified submarket matrices, preserving the requirement that a covariance matr...

In this paper we investigate the properties of the covariance matrices associated with variational Bayesian approximations, based on data from mixture models, and compare them with the true covariance matrices, corresponding to Fisher information matrices. It is shown that the covariance matrices from the variational Bayes approximations are normally ‘too small’ compared with those for the maxi...

We present some methods for graphing distributions of covariance matrices and demonstrate them on several models, including the Wishart, inverse-Wishart, and scaled inverse-Wishart families in different dimensions. Our visualizations follow the principle of decomposing a covariance matrix into scale parameters and correlations, pulling out marginal summaries where possible and using two and thr...