Reconstructing Distances Among Objects from Their Discriminability: Ehtibar N. Dzhafarov & Hans Colonius
As discussed in Chapter 1. the notion of a perceiver has a variety of possible meanings, including even cases of ~~paper-and-pencil" perceivers, abstract computational procedures assigning to every pair x. y the probability "~..' (x, y) (subject to R,egular 1tIinirnality). The exanlple given in Chapter 1 was that of~' (x, y) being the probability \vith which a data set (in a particular format) generated by a statistical lllodel, x. rejects (in accordance with some criterion) a generally different statistical rnodel, y. The pairwise determinations of sanleness/difference in this exarnple (meaning, model y is retained/rejected when applied to a data set generated by model x) are usually readily available and simple. It is an attractive possibility, therefore, to have a general algorithnl in which one can use these pairwise determinations to compute distances aillong conceptual objects (here, statistical models). The alternative, an a priori choice of a distance llleasure between two statistical models, may be less obvious and nlore difficult to justify.