  The estimation of Bayesian networks given high-dimensional data, in
particular 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 identically
distributed samples. However, it is often the case that the available data have
a more complex mean structure plus additional components of variance, which
must then be accounted for in the estimation of a Bayesian network. In this
paper, score metrics that take account of such complexities are proposed for
use in conjunction with score-based methods for the estimation of Bayesian
networks. We propose firstly, a fully Bayesian score metric, and secondly, a
metric inspired by the notion of restricted maximum likelihood. We demonstrate
the performance of these new metrics for the estimation of Bayesian networks
using simulated data with known complex mean structures. We then present the
analysis of expression levels of grape berry genes adjusting for exogenous
variables believed to affect the expression levels of the genes. Demonstrable
biological effects can be inferred from the estimated conditional independence
relationships and correlations amongst the grape-berry genes.
