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Perhaps the strongest arguments for objective Bayesianism were given by Edwin T.Jaynes, based mainly on the consequences of symmetries and on the principle of maximum entropy.Some attempts have been made at finding a priori probabilities, i.e.

It would therefore be odd to choose a prior for which a permutation of the labels would cause a change in our predictions about which cup the ball will be found under; the uniform prior is the only one which preserves this invariance.When a family of conjugate priors exists, choosing a prior from that family simplifies calculation of the posterior distribution.Parameters of prior distributions are a kind of hyperparameter.For example, if one uses a beta distribution to model the distribution of the parameter p of a Bernoulli distribution, then: An informative prior expresses specific, definite information about a variable.An example is a prior distribution for the temperature at noon tomorrow.

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