Combining Statistical Models

This paper develops a general framework to support the combination of information from independent but related experiments, by introducing a formal way of combining statistical models represented by families of distributions. A typical example is the combination of multivariate Gaussian families respecting conditional independence constraints, i.e. Gaussian graphical models. Combining information from such models, represented by their dependence graphs, yields a formal basis for what could suitably be termed structural meta analysis. We consider issues of combination of pairs of distributions, extending the concept of meta-Markov combination introduced by Dawid and Lauritzen. The proposed theory is then applied to the special case of graphical models.