 This kind of situation may, of course, arise for much more complex hypotheses. The alternative hypotheses of interest may be deterministic physical theories, say Newtonian Gravitation Theory and some specific alternatives.  Some of the experiments that test this theory relay on somewhat imprecise measurements that have known statistical error characteristics, which are expressed as part of the background or auxiliary hypotheses, \(b\). For example, the auxiliary \(b\) may describe the error characteristics of a device that measures the torque imparted to a quartz fiber, where the measured torque is used to assess the strength of the gravitational force between test masses. In that case \(b\) may say that for this kind of device the measurement errors are normally distributed about whatever value a given gravitational theory predicts, with some specified standard deviation that is characteristic of the device. This results in specific values \(r_i\) for the likelihoods, \(P[e \pmid h_i\cdot b\cdot c] = r_i\), for each of the various gravitational theories, \(h_i\), being tested.