type="main" xml:id="rssb12062-abs-0001"> <title type="main">Summary</title> <p>The essentials of our paper of 2002 are briefly summarized and compared with other criteria for model comparison. After some comments on the paper's reception and influence, we consider criticisms and proposals forimprovement made by us and others.

We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure "p"_"D" for the effective number of parameters in a model as the difference between the posterior mean of the...