  Gaussian graphical model is a graphical representation of the dependence
structure for a Gaussian random vector. It is recognized as a powerful tool in
different applied fields such as bioinformatics, error-control codes, speech
language, information retrieval and others. Gaussian graphical model selection
is a statistical problem to identify the Gaussian graphical model from a sample
of a given size. Different approaches for Gaussian graphical model selection
are suggested in the literature. One of them is based on considering the family
of individual conditional independence tests. The application of this approach
leads to the construction of a variety of multiple testing statistical
procedures for Gaussian graphical model selection. An important characteristic
of these procedures is its error rate for a given sample size. In existing
literature great attention is paid to the control of error rates for incorrect
edge inclusion (Type I error). However, in graphical model selection it is also
important to take into account error rates for incorrect edge exclusion (Type
II error). To deal with this issue we consider the graphical model selection
problem in the framework of the multiple decision theory. The quality of
statistical procedures is measured by a risk function with additive losses.
Additive losses allow both types of errors to be taken into account. We
construct the tests of a Neyman structure for individual hypotheses and combine
them to obtain a multiple decision statistical procedure. We show that the
obtained procedure is optimal in the sense that it minimizes the linear
combination of expected numbers of Type I and Type II errors in the class of
unbiased multiple decision procedures.
