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So I'm trying to solve a problem with Bayesian networking. I know the conditional probabilities of some event, say that it will rain. Suppose that I measure (boolean) values from each of four sensors (A1 - A4). I know the probability that of rain and I know the probability of rain given the measurements on each of the sensors.

Now I add in a new twist. A4 is no longer available, but B1 and B2 are (they are also boolean sensors). I know the conditional probabilities of both B1 and B2 given the measurement of A4. How do I incorporate those probabilities into my Bayesian network to replace the lost data from A4?

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Your problem fits perfectly to Multi-Entity Bayesian Networks (MEBN). This is an extension to standard BN using First Order Logic (FOL). It basically allows nodes to be added and/or removed based on the specific situation at hand. You define a template for creating BN on the fly, based on the current knwoledge available.

There are several papers on it available on the Web. A classic reference to this work is "Multi-Entity Bayesian Networks Without Multi-Tears".

We have implemented MEBN inside UnBBayes. You can get a copy of it by following the instructions @ http://sourceforge.net/p/unbbayes/discussion/156015/thread/cb2e0887/. An example can be seen in the paper "Probabilistic Ontology and Knowledge Fusion for Procurement Fraud Detection in Brazil" @ http://link.springer.com/chapter/10.1007/978-3-642-35975-0_2.

If you are interested in it, I can give you more pointers later on.

Cheers, Rommel

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