Bayesian Statistics

Available observations generally consist of (possibly many) sets of data of the general form D = { x 1 , … , x n }, where the x i ’s are somewhat “homogeneous” (possibly multidimensional) observations x i . Statistical methods are then typically used to derive conclusions on both the nature of the process which has produced those observations, and on the expected behavior at future instances of the same process. A central element of any statistical analysis is the specification of a probability model which is assumed to describe the mechanism which has generated the observed data D as a function of a (possibly multidimensional) parameter (vector) ω ∈ Ω, sometimes referred to as the state of nature , about whose value only limited information (if any) is available. All derived statistical conclusions are obviously conditional on the assumed probability model.