Abstract
FOR the last two hundred years the attention of logicians and mathematicians has been directed to the inverse principles of the theory of probability, in which we reason from known events to possible causes. Two different methods of calculation are in use, which give approximately the same results. According to the celebrated theorem of James Bernoulli, “If a sufficiently large number of trials is made, the ratio of the favourable to the unfavourable events will not differ from the ratio of their respective probabilities beyond a certain limit in excess or defect, and the probability of keeping within these limits, however small, can be made as near certainty as we please by taking a sufficiently large number of trials.” The inverse use of this theorem is much more important and much more liable to objection and difficulties than the direct use. In the words of De Morgan, “When an event has happened, and may have happened in two or three different ways, that way which is most likely to bring about the event, is most likely to have been the cause.”
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LUPTON, S. Michell's Problem . Nature 38, 272–274 (1888). https://doi.org/10.1038/038272a0
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DOI: https://doi.org/10.1038/038272a0