The Laplace Rule of Succession under a General Prior
by Kalyan Raman
Laplace's rule of succession has often been invoked by scientists to probabilistically justify inductive inferences. A common criticism of the rule is its dependence on a uniform prior distribution. Such a distribution is totally noninformative and implies that the researcher's prior knowledge is minimal. This paper shows that the Laplace rule can be generalized to the more realistic case where the researcher has an informative prior distribution. Informative priors lead to a generalized rule of succession which is a linear combination of Laplacian rules; furthermore this generalized rule retains those critical features of Laplace's result which have been used to justify inductive inferences.
Laplace's Rule of Succession, Bayesian Inference, Probability, Induction, Beta distribution
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