Analysis of densities
GEORGE A. TOMLINSON · Library and Archives Canada (Government of Canada) · 1998
A fully Bayesian method is developed for modelling the distribution of probability density functions across a population. We call it "analysis of densities" to emphasize the similarity with analysis of variance. The di#erence is that the usual analysis of variance models the variance of a scalar across subjects and here we model the variability of probability density functions across subjects. The probability density functions for di#erent subjects are modelled as mixtures of Dirichlet processes. A common baseline prior distribution for the mixing distribution is assumed. The similarity between density estimates for di#erent subjects is controlled by the precision parameters of the subjectspecific Dirichlet processes. The common baseline prior is also estimated using a mixture-of-Dirichlet-processes model. For this second Dirichlet process, the precision parameter controls how much detail from the individual density estimates is captured in the estimate of the baseline prior. Fitting t...