BNs

BNs are well researched statistical models. In particular, functions for computing the likelihood of models have been known for some time. Therefore, they were chosen to be the first model space tackled in our framework. Our work relates to that of [Friedman KollerFriedman Koller2000]. However, the benefit of using SLPs for defining the whole model space is that complicated and precise priors including hard constraints and statistically expressed preferences can be defined. This is an area with very little attention in the literature, where it is normal to assume a uniform, uninformative, prior.

BN related files are stored in mcmcms/bns/. The generator SLPs are in slps/ and it is worthwhile noting that most of them have failure-free versions. This is a particularly important for the BP and CP proposals (Section 5.1) which were what we originally used with these SLPs. You can run queries run_test. and run_disp. from files run_test.pl and run_disp.pl for small demonstrations. The likelihood used was:

$$\prod_{j \in \mathbf{u}_{i}} \frac{\Gamma(\alpha_{ij})}{\G... ... \frac{\Gamma(\alpha_{ijk} + N_{ijk})}{\Gamma(\alpha_{ijk})}$$ (3)

and it can be found in bns/src/llhood/lhood_canonical_uai01.pl. (For details see [Angelopoulos CussensAngelopoulos Cussens2001].) Various auxiliary programs for manipulating BNs and the generated output can be found in bns/auxiliary/.