Hypercausality, randomisation, and local and global independence
UNSPECIFIED (2004) Hypercausality, randomisation, and local and global independence. In: 1st European Workshop on Probabilistic Graphical Models (PGM 02), Cuenca, SPAIN, NOV, 2002. Published in: ADVANCES IN BAYESIAN NETWORKS, 146 pp. 1-18.Full text not available from this repository.
In this paper we define the multicausal essential graph. Such graphical model demands further properties an equivalence class of Bayesian networks (BNs). In particular, each BN in an equivalence class is assumed to be causal in a stronger version of the manipulation causality of Spirtes et al (1993). In practice, the probabilities of any causal Bayesian network (CBN) will usually need to be estimated. To estimate the conditional probabilities in BNs it is common to assume local and global independence. The first result we prove in this paper is that if the BN is believed to be causal in a sufficiently strong sense i.e., is hypercausal, then it is necessary to make the assumption of local and global prior independence. Our second theorem develops this result. We give a characterisation of prior distributions sympathetic to causal hypotheses on all BNs in the equivalence class defined by an essential graph. We show that such strongly causally compatible priors satisfy a generalisation of the Geiger and Heckerman (1997) condition. In a special case when the essential graph is undirected, this family of prior distributions reduces to the Hyper-Dirichlet family, originally introduced by Dawid and Lauritzen (1993) as a prior family for decomposable graphical models.
|Item Type:||Conference Item (UNSPECIFIED)|
|Subjects:||Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Q Science > QA Mathematics
|Series Name:||STUDIES IN FUZZINESS AND SOFT COMPUTING|
|Journal or Publication Title:||ADVANCES IN BAYESIAN NETWORKS|
|Editor:||Gamez, JA and Moral, S and Salmeron, A|
|Number of Pages:||18|
|Page Range:||pp. 1-18|
|Title of Event:||1st European Workshop on Probabilistic Graphical Models (PGM 02)|
|Location of Event:||Cuenca, SPAIN|
|Date(s) of Event:||NOV, 2002|
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