Quantum theory as a description of robust experiments: derivation of the Pauli equation

It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically independent, and (iii) the observed frequency distributions are robust with respect to small changes in the conditions under which the experiment is carried out. The derivation does not take recourse to concepts of quantum theory and is based on the same principles which have already been shown to lead to e.g. the Schr\"odinger equation and the probability distributions of pairs of particles in the singlet or triplet state. Application to Stern-Gerlach experiments with chargeless, magnetic particles, provides additional support for the thesis that quantum theory follows from logical inference applied to a well-defined class of experiments.