Foundations of Bayesian Statistics

Abstract

In three basic points Bayesian statistics differs from traditional statistics. First Bayesian statistics is founded on Bayes’theorem. By this theorem unknown parameters are estimated, confidence regions for the unknown parameters are established and hypotheses for the parameters are tested. Furthermore, Bayesian statistics extends the notion of probability by defining the probability for statements or propositions. The probability is a measure for the plausibility of a statement. Finally, the unknown parameters of Bayesian statistics are random variables. But nevertheless, the unknown parameters can represent constants. There are numerous applications of Bayesian statistics for the analysis of geodetic data, some of them are pointed out.