Physical Sciences and Mathematics Commons^™

Computing Highly Accurate Confidence Limits From Discrete Data Using Importance Sampling, Chris Lloyd

Chris J. Lloyd

For discrete parametric models, approximate confidence limits perform poorly from a strict frequentist perspective. In principle, exact and optimal confidence limits can be computed using the formula of Buehler (1957), Lloyd and Kabaila (2003). So-called profile upper limits (Kabaila \& Lloyd, 2001) are closely related to Buehler limits and have extremely good properties. Both profile and Buehler limits depend on the probability of a certain tail set as a function of the unknown parameters. Unfortunately, this probability surface is not computable for realistic models. In this paper, importance sampling is used to estimate the surface and hence the confidence limits. …