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Rule of succession - Wikipedia

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In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem.[1] The formula is still used, particularly to estimate underlying probabilities when there are few observations or events that have not been observed to occur at all in (finite) sample data. If we repeat an experiment that we know can result in a success or failure, n times independently, and get s successes, and n − s failures, then what is the probability that the next repetition will succeed? More abstractly: If X1, ..., Xn+1 are conditionally independent random variables that each can assume the value 0 or 1, then, if we know nothing more about them, Since we have the prior knowledge that we are looking at an experiment for which both success and failure are possible, our estimate is as if we had observed one success and one failure for sure before we even started the experiments. In a sense we made n + 2 observations (know

Rule of succession - Wikipedia Jump to content From Wikipedia, the free encyclopedia Formula in probability theory This article is about the rule of succession in probability theory. For monarchical and presidential rules of succession, see Order of succession . "Laplace–Bayes estimator" redirects here. For statistical estimators that maximize posterior expected utility or minimize posterior expected loss, see Bayes estimator . This article needs more citations . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . Find s

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