Evaluation of astrophysical hypotheses.

The aim of this article is to set out a bookkeeping procedure for formalizing the process of asessing a hypothesis by comparison of conclusions drawn theoretically from this hypothesis with facts obtained by reduction of observational data. The formalism used is that of probability theory. A key role is played by Bayes's rule representing the inductive process of adjusting a degree of belief in response to new information. The foliowing model is used. Between observation and theory is an interface'' which comprises a number of independent items. Each item comprises a set of mutually exclusive statements. Probabilities assigned to statements of an item by reduction of observational data comprise a fact''. Probabilities assigned to statements of an item by theoretical analysis of a considered hypothesis represent a conclusion'' drawn from that hypothesis. Each fact should be free from theoretical bias and each conclusion free from observational bias. The model requires that one consider a complete set of mutually exculsive hypotheses. Where this cannot be done explicitly, it may be achieved by the introduction of a null hypothesis'' or igonance hypothesis.'' Conclusions'' drawn from this hypothesis are chosen to be maximally noncommittal. Formulae are derived which show (a) how the probabilitymore » of each hypothesis should be adjusted in response to information concerning one item, and (b) how such estimates concerning more than one item may be combined. The procedure is illustrated by a work sheet'' showing how a few facts and conclusions concerning pulsars were he neutron-star and white-dwarf hypotheses. (auth)« less