foundations of computational agents
The general case is with unknown structure, hidden variables, and missing data; we may not even know which variables should be part of the model. Two main problems arise. The first is the problem of missing data discussed earlier. The second problem is computational; although there may be a well-defined search space, it is prohibitively large to try all combinations of variable ordering and hidden variables. If one only considers hidden variables that simplify the model (as seems reasonable), the search space is finite, but enormous.
One can either select the best model (e.g, the model with the highest posterior probability) or average over all models. Averaging over all models gives better predictions, but it is difficult to explain to a person who may have to understand or justify the model.