To infer knowledge from a Bayesian network, we use Bayesian inference. First we introduce some terminology:
Prior Odds are predictive support with only background knowledge:
Likelihood Ratio is diagnostic support given to H by observed evidence:
Posterior Odds are predictive support given observed evidence, e:
By using these definitions, we can infer knowledge like in probability theory. We illustrate this with an example:
A salesman has installed an alarm in a shop, and it is known that the alarm obeys these probabilities:
P(Burgulary) = 10-4
To find the probability that it is a burglar if the alarm goes, we do the following: First we find the posterior odds of it being a burglar:
To convert odds to probability, we use: (deducted from the prior odds)
This implies: