Approaches to Inverse Linear Regression. Revision

摘要

Many measurement problems can be formulated as follows: First, a certain linear relationship between two variables is to be estimated by using pairs of input and output data; thereafter, the value of an unknown input variable is to be estimated given an observation of the corresponding output variable. This problem is often referred to as inverse regression or discrimination. In this paper first non-Bayesian approaches to the problem, thereafter the Bayesian approach by Hoadley are presented. Third, a Bayesian approach by Avenhaus and Jewell is discussed which uses the ideas of credibility theory. Finally, a new Bayesian approach is presented. The advantages and disadvantages of the various approaches are put together. (Author)