This paper deals with the problem of increasing the efficiency of Monte Carlo calculations. The methods of doing so permit one to reduce the sample size required to produce estimates of a fixed level of accuracy or, alternatively, to increase the accuracy of the estimates for a fixed cost of computation. Few theorems are known with regard to optimal sampling schemes, but several helpful ideas of very general applicability are available for use in designing Monte Carlo sampling schemes. Three of these ideas are discussed and illustrated in simple cases. These ideas are (1) correlation of samples, (2) importance sampling, and (3) statistical estimation. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
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White Plains, N. Y. Sir: William Lee Miller's discussion of my book, On Thermonuclear War, appearing in your April issue (which only recently came to my attention), impressed me quite favorably. I am grateful to Mr. Miller for expressing approval of some of my points and for defending me against what he terms the "absurd. .. naive reaction against writers. .. [that] blames them somehow for the world they discuss." Mr. Miller criticizes my book not for immorality but for amorality. Actually I am very sympathetic with his major thesis, and I would like to add a few words in order to clarify my position and, hopefully, some of the discussion. Mr. Miller is emphatically right that "thermonuclear war is too important a subject to be left to the game-theorists." Although game theory can make some contribution to the understanding of certain problems that arise in the real world, the contribution is at best a very small part of what is necessary, and in fact I made no use of formal game theory in the book. I would conjecture that most of the animosity that critics of defense literature have directed against the use of game theory is really aimed at(as far as it is aimed at anything) what the critic considers to be an excessive use of rationality. I personally believe that the current discussion of these problems could only be improved by the judicious injection of rational arguments. Mr. Miller says that "the technical-mathematical treatment of social problems.. . can yield important knowledge, but at the highest moral and philosophical level, of course, it is fatally defective." I agree, at least, that at the moral level a technical approach is not enough. My reason for using objective methodologies to study thermonuclear war was simply the hope that they would "yield important knowledge." Such knowledge is indispensable to moral and philosophical understanding if it is not to be founded on ignorance or error. Again, it is my belief that much of the current discussion suffers from misinformation as well as irrationality. My book was specifically addressed to the technical side of the problem and to professional students of the subject. 1 have good reason to believe that it has had an important effect on many of those who were not enough aware of the dangers of the arms race and the serious and complex military, political and social problems of strategists that risk the use of nuclear weapons. While I agree that there is "a basic moral revulsion [to weapons of mass destruction] that should not be overcome," to weaken the discus
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