Topic summary
Compound distribution
Extracted from the Wikipedia article Compound probability distribution.
Bayesian inference
Besides ubiquitous marginal distributions that may be seen as special cases of compound distributions, in Bayesian inference, compound distributions arise when, in the notation above, F represents the distribution of future observations and G is the posterior distribution of the parameters of F, given the information in a set of observed data. This gives a posterior predictive distribution. Correspondingly, for the prior predictive distribution, F is the distribution of a new data point while G is the prior distribution of the parameters.