New insights on stochastic complexity

The Minimum Description Length (MDL) principle led to various expressions of the stochastic complexity (SC), and the most recent one is given by the negative logarithm of the Normalized Maximum Likelihood (NML). For better understanding the properties of the newest SC-formula, we relate it to the well-known Generalized Likelihood Ratio Test (GLRT). Additionally, we compare the SC with the Bayesian Information Criterion (BIC) and other model selection rules. Some of the results are discussed in connection with families of models that are widely used in signal processing.