Randomness, probability, and likelihood

Abstract

In most cases a physical object responds with different data on different occasions, even when subject to the same stimulus. The difference may be small enough to be negligible, but often it is not. Unless there is a change in response because the object depends on time t in a particular way that one would also like to model, one is faced with the following situation: One knows that response data is random, but one also expects that there is some information in the data that will be invariant and will hold also in the application phase. This information is obviously the most comprehensive ‘model’ one can ever get out of the particular data set, and any design for the application phase must be based on that invariant information. The problem of model making is then to represent the information in terms of what one knows, i.e. model structure (if the modelling part has been done), experiment specifications, and data, so that one can compute something. A way to find a computable representation is to use probabilistic concepts, stochastic variables, and the socalled ‘Bayesian approach’.