This follows from the fact that the full conditional distribution is proportional to the joint distribution. If the child nodes of the collapsed nodes are continuous, this distribution will generally not be of a known form, and may well be difficult to sample from despite the fact that a closed form can be written, for the same reasons as described above for non-well-known compound distributions. However, in the particular case that the child nodes are discrete, sampling is feasible, regardless of whether the children of these child nodes are continuous or discrete. In fact, the principle involved here is described in fair detail in the article on the Dirichlet-multinomial distribution. It is also possible to extend Gibbs sampling in various ways. For example, in the case of variables whose conditional distribution is not easy to sample from, a single iteration of slice sampling or the Metropolis–Hastings algorithm can be used to sample from the variables in question. A more efficient alternative is the application of the adaptive rejection sampling (ARS) methods for sampling from the full-conditional densities. When the ARS techniques cannot be applied, the adaptive rejection Metropolis sampling algorithms are often employed. Furthermore, other alternatives can be found in literature. The auxiliary samples generated by the internal sampler (such as the MH and ARMS schemes) can be recycled within the final Gibbs estimators, improving their efficiency with no extra cost (the so-called Recycling Gibbs sampling procedure ). It is also possible to incorporate variables that are not random variables, but whose value is deterministically computed from other variables. Generalized linear models, e.g. logistic regression (aka "maximum entropy models"), can be incorporated in this fashion. (BUGS, for example, allows this type of mixing of models.) There are two ways that Gibbs sampling can fail. The first is when there are islands of high-probability states, with no paths between them. For example, consider a probability distribution over 2-bit vectors, where the vectors (0,0) and (1,1) each have probability ½, but the other two vectors (0,1) and (1,0) have probability zero. Gibbs sampling will become trapped in one of the two high-probability vectors, and will never reach the other one. More generally, for any distribution over high-dimensional, real-valued vectors, if two particular elements of the vector are perfectly correlated (or perfectly anti-correlated), those two elements will become stuck, and Gibbs sampling will never be able to change them.