  A classic application of description length is for model selection with the
minimum description length (MDL) principle. The focus of this paper is to
extend description length for data analysis beyond simple model selection and
sequences of scalars. More specifically, we extend the description length for
data analysis in Gaussian graphical models. These are powerful tools to model
interactions among variables in a sequence of i.i.d Gaussian data in the form
of a graph. Our method uses universal graph coding methods to accurately
account for model complexity, and therefore provide a more rigorous approach
for graph model selection. The developed method is tested with synthetic and
electrocardiogram (ECG) data to find the graph model and anomaly in Gaussian
graphical models. The experiments show that our method gives better performance
compared to commonly used methods.
