Sampling.

The procedure for sampling from a mixture of trees is a two stage process: first one samples a value $k$ for the choice variable $z$ from its distribution $(\lambda_1, \lambda_2, \ldots \lambda_m)$, then a value $x$ is sampled from $T^k$ using the procedure for sampling from a tree distribution. In summary, the basic operations on mixtures of trees, marginalization, conditioning and sampling, are achieved by performing the corresponding operation on each component of the mixture and then combining the results. Therefore, the complexity of these operations scales linearly with the number of trees in the mixture.