Bayesian goodness of fit assessment through posterior deviances
by Murray Aitkin
Abstract: Assessing the goodness of fit of observed data to a statistical model is an important part of model validation, or model criticism. We assess goodness of fit through comparing the frequencies n j of observations from a single sample, falling in J discrete categories, with frequencies specified by a statistical model.
We compare the null and alternative (multinomial) models through their posterior deviance distributions (Dempster 1974, 1997, Aitkin 1997, Aitkin, Boys and Chadwick 2005) rather than through a Bayes factor. This approach works equally well for continuous and for discrete data, and we apply it to several examples.
The computational method requires no more than standard Monte Carlo simulations from the Dirichlet and other standard posterior distributions: we use diffuse priors for the parameters of the distributions being compared.
For More Information: Guoqi Qian email@example.com