Taking into account causal relations of the environment usually
results in simpler and computationally efficient models. Take for
example a situation where *A* and *B* are known to affect *C* and *D*,
but the effect is causally mediated through *E*. If *E* summarises
all the knowledge that *A* and *B* have about *C* and *D*, then *C*and *D* are conditionally independent of *A* and *B* given *E*.
Mathematically this means that

(23) |

It would be possible to consider the situation from the point of view of only the variables

In general, a model with more variables but with simpler dependences
is computationally more efficient. Introducing mediating variable *E*simplifies the dependences because either only one variable affects
two others, as in
*P*(*CD* | *E*_{i}), or two variables affect one, as in
*P*(*E*_{i} | *AB*). This strategy is a second nature to human beings who
constantly try to organise the world by splitting complex dependences
into simpler ones by introducing hidden, mediating variables, and
therefore it is also usually easy to construct models using the same
design principle. The mediating variables are not directly observable
but can only be inferred from the dependence structure of the
observations. These variables are therefore often called hidden or
latent variables [25].

From a computational point of view, the efficiency is caused by the fact that the posterior probability of the unknown variables will be a product of many simple terms. Taking the logarithm will then split the product into a sum of many simple terms. Most methods for approximating the posterior probabilities can make use of this property, including the ML and MAP estimators, the EM algorithm, Laplace's method, ensemble learning and many versions of stochastic sampling.