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Implementing (Multiple) Monte Carlo Tests

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Consider Monte Carlo tests, e.g. bootstrap tests or permutation tests. Naive implementations can lead to decisions that depend mainly on the simulation error and not on the observed data. This talk will present algorithms that solve this problem: for individual Monte Carlo tests as well as for multipe Monte Carlo tests with multiplicity correction such as the Benjamini & Hochberg False Discovery Rate (FDR) procedure. The key property of the presented algorithms is that, with arbitrarily high probability, the same decisions as the original procedure with the ideal p-values is reached.

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