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An informative prior expresses specific, definite information about a variable. An example is a prior distribution for the temperature at noon tomorrow. A reasonable approach is to make the prior a normal distribution with expected value equal to today's noontime temperature, with variance equal to the day-to-day variance of atmospheric temperature, or a distribution of the temperature for ...
The term prior may refer to: Prior (ecclesiastical), the head of a priory (monastery) Prior convictions, the life history and previous convictions of a suspect or defendant in a criminal case; Prior probability, in Bayesian statistics; Prior knowledge for pattern recognition; Saint Prior (4th century), an Egyptian hermit and disciple of Anthony ...
The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability , such as the frequentist interpretation, which views probability as the limit of the relative frequency of an event after ...
Prior consistent statements and prior inconsistent statements, in the law of evidence, occur where a witness, testifying at trial, makes a statement that is either consistent or inconsistent, respectively, with a previous statement given at an earlier time such as during a discovery, interview, or interrogation.
The metaphysical distinction between necessary and contingent truths has also been related to a priori and a posteriori knowledge.. A proposition that is necessarily true is one in which its negation is self-contradictory; it is true in every possible world.
In Bayesian probability theory, if, given a likelihood function (), the posterior distribution is in the same probability distribution family as the prior probability distribution (), the prior and posterior are then called conjugate distributions with respect to that likelihood function and the prior is called a conjugate prior for the likelihood function ().
In Bayesian statistics, the Jeffreys prior is a non-informative prior distribution for a parameter space. Named after Sir Harold Jeffreys , [ 1 ] its density function is proportional to the square root of the determinant of the Fisher information matrix:
A prior distribution of α and β is thus a hyperprior. In principle, one can iterate the above: if the hyperprior itself has hyperparameters, these may be called hyperhyperparameters, and so forth. One can analogously call the posterior distribution on the hyperparameter the hyperposterior, and, if these are in the same family, call them ...