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Conservative hypothesis tests and confidence intervals using importance sampling


  • Matthew T. Harrison


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. Copyright 2012, Oxford University Press.

Suggested Citation

  • Matthew T. Harrison, 2012. "Conservative hypothesis tests and confidence intervals using importance sampling," Biometrika, Biometrika Trust, vol. 99(1), pages 57-69.
  • Handle: RePEc:oup:biomet:v:99:y:2012:i:1:p:57-69

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