We consider discrete causal DAG-models (or Bayesian Networks) wherein the ordering of the variables is fixed across model structures. Given a prior on the parameter space of a model we describe a method for deriving a compatible prior on the parameter space of a submodel. This allows to generate automatically compatible priors for model parameters starting from a single prior relative to the largest entertained model. Our method makes use of a general procedure for constructing compatible priors for causal DAG-models, named reference conditioning, which is invariant within a suitable class of re-parameterisations and is model intrinsic. We show that if the generating prior satisfies global parameter independence, so does the compatible prior; in addition, prior modularity holds. Further results are obtained when the starting prior is product Dirichlet. A simple illustration of the methodology, and comparisons with alternative methods, are presented.
|Titolo della pubblicazione ospite||Bayesian Statistics 7|
|Editor||A. F. M. Smith Editor, Mike West D. Heckerman Editor, M. J. BAYARRI, A. P. DAWID, J. O. BERGER, D. HECKERMAN, A.F.M. SMITH, W. WEST, G G|
|Numero di pagine||12|
|Stato di pubblicazione||Pubblicato - 2003|
- Graphical model
- Prior distribution