© 1991 by Biometrika Trust
Sequential Monte Carlo p-values
1Department of Mathematics and Statistics, University of Newcastle upon Tyne Newcastle upon Tyne NE1 7RU, U.K.
2Department of Statistics, University of Oxford 1 South Parks Road, Oxford OX1 3TG, U. K.
The assessment of statistical significance by Monte Carlo simulation may be costly in computer time. This paper looks at a number of ways of calculating exact Monte Carlo p-values by sequential sampling. Such p-values are shown to have properties similar to those obtained by sampling with a fixed sample size. Both standard and generalized Monte Carlo procedures are discussed and, in particular, a sequential method is proposed for dealing with situations in which values can only be conveniently generated using a Markov chain, conditioned to pass through the observed data.
Key Words: Monte Carlo testing • Markov chain • p-value • Sequential estimation • Sequential test • Significance test
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