Editing Bayesian network (section)

===Inferring unobserved variables===
Because a Bayesian network is a complete model for its variables and their relationships, it can be used to answer probabilistic queries about them. For example, the network can be used to update knowledge of the state of a subset of variables when other variables (the ''evidence'' variables) are observed. This process of computing the ''posterior'' distribution of variables given evidence is called probabilistic inference. The posterior gives a universal [[sufficient statistic]] for detection applications, when choosing values for the variable subset that minimize some expected loss function, for instance the probability of decision error. A Bayesian network can thus be considered a mechanism for automatically applying [[Bayes' theorem]] to complex problems.

The most common exact inference methods are: [[variable elimination]], which eliminates (by integration or summation) the non-observed non-query variables one by one by distributing the sum over the product; [[Junction tree algorithm|clique tree propagation]], which caches the computation so that many variables can be queried at one time and new evidence can be propagated quickly; and recursive conditioning and AND/OR search, which allow for a [[space–time tradeoff]] and match the efficiency of variable elimination when enough space is used. All of these methods have complexity that is exponential in the network's [[treewidth]]. The most common [[approximate inference]] algorithms are [[importance sampling]], stochastic [[Markov chain Monte Carlo|MCMC]] simulation, mini-bucket elimination, [[loopy belief propagation]], [[generalized belief propagation]] and [[variational Bayes|variational methods]].