In genome-wide prediction, independence of marker allele substitution effects is typically assumed; however, several biological phenomena suggest the existence of correlated effects. In statistics, graphical models have been identified as a useful and powerful tool for covariance estimation in high dimensional problems and this area is currently experiencing a great expansion. In particular, in Gaussian concentration graph models (GCGM), the distribution of a set of random variables, the marker effects in this case, is assumed to be Markov with respect to an undirected graph. On the other hand, in Gaussian covariance graph models (GCovGM), an undirected graph is used to encode the marginal covariance structure of these random variables. These models are developed to estimate the precision (GCGM) or the covariance (GCovGM) matrix of an observable p-dimensional vector-valued random variable using a sample of size N. However, in genome-wide prediction the target is to estimate the covariance or the precision matrix of an unobservable p-dimensional vector-valued random variable along with other dispersion parameters and to predict marker effects, typically using a single n-dimensional vector of phenotypes.

In this talk, we develop Bayesian and frequentist methods adapting the theory of GCGM and GCovGM to genome-wide prediction. Different approaches to define the graph based on domain-specific knowledge are proposed, and two propositions and a corollary establishing conditions to find decomposable graphs are proven. Furthermore, the scenario of unknown graph is also addressed. To this end, covariance selection methods are developed. Our approaches are promising because they allow incorporation of biological information in the prediction process, and because they are more flexible and general than other methods accounting for correlated marker effects that have been proposed previously.