Editing Bayesian network (section)

===Parameter learning===
In order to fully specify the Bayesian network and thus fully represent the [[joint probability distribution]], it is necessary to specify for each node ''X'' the probability distribution for ''X'' conditional upon ''X''{{'s}} parents. The distribution of ''X'' conditional upon its parents may have any form. It is common to work with discrete or [[normal distribution|Gaussian distributions]] since that simplifies calculations. Sometimes only constraints on distribution are known; one can then use the [[principle of maximum entropy]] to determine a single distribution, the one with the greatest [[information entropy|entropy]] given the constraints. (Analogously, in the specific context of a [[dynamic Bayesian network]], the conditional distribution for the hidden state's temporal evolution is commonly specified to maximize the [[entropy rate]] of the implied stochastic process.)

Often these conditional distributions include parameters that are unknown and must be estimated from data, e.g., via the [[maximum likelihood]] approach. Direct maximization of the likelihood (or of the [[posterior probability]]) is often complex given unobserved variables. A classical approach to this problem is the [[expectation-maximization algorithm]], which alternates computing expected values of the unobserved variables conditional on observed data, with maximizing the complete likelihood (or posterior) assuming that previously computed expected values are correct. Under mild regularity conditions, this process converges on maximum likelihood (or maximum posterior) values for parameters.

A more fully Bayesian approach to parameters is to treat them as additional unobserved variables and to compute a full posterior distribution over all nodes conditional upon observed data, then to integrate out the parameters. This approach can be expensive and lead to large dimension models, making classical parameter-setting approaches more tractable.