Importance sampling method for Feldman-Cousins confidence intervals

In various high-energy physics contexts, such as neutrino-oscillation experiments, several assumptions underlying the typical asymptotic confidence interval construction are violated, such that one has to resort to computationally expensive methods like the Feldman-Cousins method for obtaining confidence intervals with proper statistical coverage. By construction, the computation of intervals at high confidence levels requires fitting millions or billions of pseudoexperiments, while wasting most of the computational cost on overly precise intervals at low confidence levels. In this work, a simple importance sampling method is introduced that reuses pseudoexperiments produced for all tested parameter values in a single mixture distribution. This results in a significant error reduction on the estimated critical values, especially at high confidence levels, and simultaneously yields a correct interpolation of these critical values between the parameter values at which the pseudoexperiments were produced. The theoretically calculated performance is demonstrated numerically using a simple example from the analysis of neutrino oscillations. The relationship to similar techniques applied in statistical mechanics and p-value computations is discussed.