  The normalized maximized likelihood (NML) provides the minimax regret
solution in universal data compression, gambling, and prediction, and it plays
an essential role in the minimum description length (MDL) method of statistical
modeling and estimation. Here we show that the normalized maximum likelihood
has a Bayes-like representation as a mixture of the component models, even in
finite samples, though the weights of linear combination may be both positive
and negative. This representation addresses in part the relationship between
MDL and Bayes modeling. This representation has the advantage of speeding the
calculation of marginals and conditionals required for coding and prediction
applications.
