  Automated classification methods for disease diagnosis are currently in the
limelight, especially for imaging data. Classification does not fully meet a
clinician's needs, however: in order to combine the results of multiple tests
and decide on a course of treatment, a clinician needs the likelihood of a
given health condition rather than binary classification yielded by such
methods. We illustrate how likelihoods can be derived step by step from first
principles and approximations, and how they can be assessed and selected,
illustrating our approach using fMRI data from a publicly available data set
containing schizophrenic and healthy control subjects. We start from the basic
assumption of partial exchangeability, and then the notion of sufficient
statistics and the "method of translation" (Edgeworth, 1898) combined with
conjugate priors. This method can be used to construct a likelihood that can be
used to compare different data-reduction algorithms. Despite the
simplifications and possibly unrealistic assumptions used to illustrate the
method, we obtain classification results comparable to previous, more realistic
studies about schizophrenia, whilst yielding likelihoods that can naturally be
combined with the results of other diagnostic tests.
