Modeling Uncertainty: Some Conceptual Thoughts

Abstract

The place of random experiments and stochastic models in experimental sciences is discussed first. Models of uncertainty are necessarily based on prior decisions about the randomization of either the unknown itself and/or its estimate and, as such, cannot claim to any objectivity. A safeguard for building such models is to charge them maximally with data deemed relevant to the "unknown" at hand. Another look at Bayes' relation shows that its practice requires the transfer of statistics from a calibration data set to the (prior) environment of the updating process. The If(paradigm is shown to be such transfer of calibration likelihood statistics. The paper ends with a generalization of the sequential Gaussian sim-ulation algorithm allowing for a sequence of parametric non-Gaussian conditional distributions yet with means and variances given by Sf(.