ABSTRACT
Real world often leads to the necessity of nonnormal data analysis. This issue was highly enlightened with the introduction of generalized linear models (GLM), clever extensions oflinear regressions, by Neider and Wedderburn (1972), and the Bayesian point of view on this subject can be found in chapter 1. As pointed out there, the observations are distributed in the exponential family. Hence, if we denote the observations by Yt, t = 1, ... , T then their distribution can be represented through the density (or probability function)
<X { YtBt-b(Bt)} exp <Pt (1)
In addition, a suitable link function is introduced relating the mean /-It = E(Yt IBt) = b'(Bt) to the regressor vector Ft through g(J-tt) = lit = Ffj3. Also, it is supposed that y1 , ... , YT are independent; conditionally on {3. Many nonnormalities can be accommodated in this framework, including for example the Binomial and Poisson models for counting data and Gamma distribution for positive continuous data.
