In Bayesian probability, the Jeffreys prior is a noninformative prior distribution proportional to the square root of the Fisher information: Bayesianism is the philosophical tenet that the mathematical theory of probability applies to the degree of plausibility of a statement. ... A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ... In mathematics, the principal square root of a non-negative real number is denoted and represents the non-negative real number whose square (the result of multiplying the number by itself) is . ... In statistics, the Fisher information I(θ), thought of as the amount of information that an observable random variable carries about an unobservable parameter θ upon which the probability distribution of X depends, is the variance of the score. ...
As prior and posterior are not terms used in frequentist analyses, this article uses the vocabulary of Bayesian probability and Bayesian inference.
And in the continuous case, the maximum entropy prior given that the density is normalized with mean zero and variance unity is the standard normal distribution.
The Jeffreysprior attempts to solve this problem by computing a prior which expresses the same belief no matter which metric is used.
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