title: Conservative hypothesis tests and confidence intervals using importance sampling.
abstract: Importance sampling is a common technique for Monte Carlo approximation, including that of p-values. Here it is shown that a simple correction of the usual importance sampling p-values provides valid p-values, meaning that a hypothesis test created by rejecting the null hypothesis when the p-value is at most α will also have a Type I error rate of at most α. This correction uses the importance weight of the original observation, which gives valuable diagnostic information under the null hypothesis. Using the corrected p-values can be crucial for multiple testing and also in problems where evaluating the accuracy of importance sampling approximations is difficult. Inverting the corrected p-values provides a useful way to create Monte Carlo confidence intervals that maintain the nominal significance level and use only a single Monte Carlo sample.
authors.affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, U.S.A.,  matthew_harrison@brown.edu.
authors.forename: Matthew T
authors.initials: MT
authors.lastname: Harrison