Theory and Applications of Least Squares Approximations in Bayesian Analysis

Least Squares approximations of posterior axpectations are shown to provide interesting alternatives to exact cop-mputations. The theoretical part shows how to take advantage of suitable choices of coordinates and of particular structures of the sampling process. The information extracted from smple is characterized in terms of the concept of "Least square sufficiency". Aplications to the estimation of population mean, to prediction problems, to linear models and to the estimation of distribution functions are presented to illustrate the theory and to point out how an approximation to a broader model may offer a useful altrnative to the exact solution of a narrower model