Abstract
The essential feature common to all Monte Carlo computations is that at some point we have to substitute for a random variable a corresponding set of actual values, having the statistical properties of the random variable. The values that we substitute are called random numbers, on the grounds that they could well have been produced by chance by a suitable random process. In fact, as we shall go on to describe, they are not usually produced in this way; however, this should not affect the person who has to use them, since the question he should be asking is not ‘Where did these numbers come from ?’ but ‘Are these numbers correctly distributed?’, and this question is answered by statistical tests on the numbers themselves. But even this approach runs into insuperable practical difficulties because strictly speaking it requires us to produce infinitely many random numbers and make infinitely many statistical tests on them to ensure fully that they meet the postulates. Instead we proceed with a mixture of optimism and utilitarianism: optimism, in the sense that we produce only finitely many numbers, subject them to only a few tests, and hope (with some justification) that they would have satisfied the remaining unmade tests; utilitarianism, in the sense that one of the tests that might have been applied is whether or not the random numbers yield an unbiased or a reliable answer to the Monte Carlo problem under study, and it is really only this test that interests us when we are ultimately concerned only with a final numerical solution to a particular problem.
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© 1964 J. M. Hammersley and D. C. Handscomb
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Hammersley, J.M., Handscomb, D.C. (1964). Random, Pseudorandom, and Quasirandom Numbers. In: Monte Carlo Methods. Monographs on Applied Probability and Statistics. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5819-7_3
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DOI: https://doi.org/10.1007/978-94-009-5819-7_3
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