Hierarchical two-part MDL code for multinomial distributions

We leverage the Minimum Description Length (MDL) principle as a model selection technique for multinomial distributions and suggest a two-part MDL code based on a hierarchical encoding of the multinomial parameters. We compare this code with the alternative Normalized Maximum Likelihood (NML) code and exhibit large regions of the parameter space where the hierarchical code dominates the NML one. We then present an application of the multinomial distribution to joint density estimation and show that the hierarchical code brings significant improvements.