Applied Bayesian Modelling, 2nd Edition

where are hyperparameters. They will be assigned their own prior , which will involve further unknowns.

For example, consider a Poisson model , where is the number of nonfatal illnesses or accidents in a fixed period (e.g. a year), and is a measure of illness or accident proneness. Instead of assuming all individuals have the same proneness, we might well consider allowing to vary over individuals according to a density , for instance a gamma or log-normal density to reflect the positive skewness in proneness. Since is necessarily positive, we then obtain the marginal distribution of the ...