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The estimation of Bayesian networks given high-dimensional data, inparticular gene expression data, has been the focus of much recent research.Whilst there are several methods available for the estimation of such networks,these typically assume that the data consist of independent and identicallydistributed samples. However, it is often the case that the available data havea more complex mean structure plus additional components of variance, whichmust then be accounted for in the estimation of a Bayesian network. In thispaper, score metrics that take account of such complexities are proposed foruse in conjunction with score-based methods for the estimation of Bayesiannetworks. We propose firstly, a fully Bayesian score metric, and secondly, ametric inspired by the notion of restricted maximum likelihood. We demonstratethe performance of these new metrics for the estimation of Bayesian networksusing simulated data with known complex mean structures. We then present theanalysis of expression levels of grape berry genes adjusting for exogenousvariables believed to affect the expression levels of the genes. Demonstrablebiological effects can be inferred from the estimated conditional independencerelationships and correlations amongst the grape-berry genes.

Estimating Bayesian networks for high-dimensional data with complex mean structure and random effects