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.
Leucari, V., Consonni, G., Compatible Priors for Causal Bayesian Networks, in D. Heckerman Editor, A. F. M. S. E. M. W., Bayarri, M. J., Dawid, A. P., Berger, J. O., Heckerman, D., Smith, A., West, W., G, G. (ed.), Bayesian Statistics 7, Oxford University Press, OXFORD -- GBR 2003: 596- 607 [http://hdl.handle.net/10807/14764]
Compatible Priors for Causal Bayesian Networks
Leucari, Valentina;Consonni, Guido
2003
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.