Consider two probability distributions P and Q. Usually, P represents the data, the observations, or a measured probability distribution. Distribution Q represents instead a theory, a model, a description or an approximation of P. The Kullback–Leibler divergence D KL ( P ∥ ∥ Q ) is then interpreted as the average difference of the number of bits required for encoding samples of P using a code optimized for Q rather than one optimized for P. Note that the roles of P and Q can be reversed in some situations where that is easier to compute, such as with the expectation–maximization algorithm (EM) and evidence lower bound (ELBO) computations.