Bayesian personalism,the methodology of scientific research programmes,and Duhem's problem

The detailed analysis of a particular quasi-historical numerical example is used to illustrate the way in which a Bayesian personalist approach to scientific inference resolves the Duhemian problem of which of a conjunction of hypotheses to reject when they jointly yield a prediction which is refuted. Numbers intended to be approximately historically accurate for my example show, in agreement with the views of Lakatos, that a refutation need have astonishingly little effect on a scientist's confidence in the ‘hard core’ of a successful research programme even when a comparable confirmation would greatly enhance that confidence (an initial confidence of 0.9 fell by a fraction of a percent in the refutation case and rose to only a fraction of a percent short of unity in the comparable confirmation case). Timeo Danaos et dona ferentis.