In Bayesian probability, the Jeffreys prior, named after Sir Harold Jeffreys,[1] is a non-informative prior distribution for a parameter space; its density function is proportional to the square root of the determinant of the Fisher information matrix:
It has the key feature that it is invariant under a change of coordinates for the parameter vector . That is, the relative probability assigned to a volume of a probability space using a Jeffreys prior will be the same regardless of the parameterization used to define the Jeffreys prior. This makes it of special interest for use with scale parameters.[2] As a concrete example, a Bernoulli distribution can be parametrized by the probability of occurrence p, or by the odds ratio. A naive uniform prior in this case is not invariant to this reparametrization, but the Jeffreys prior is.
In maximum likelihood estimation of exponential family models, penalty terms based on the Jeffreys prior were shown to reduce asymptotic bias in point estimates.[3][4]
^Jeffreys H (1946). "An invariant form for the prior probability in estimation problems". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 186 (1007): 453–461. Bibcode:1946RSPSA.186..453J. doi:10.1098/rspa.1946.0056. JSTOR 97883. PMID 20998741.
^Jaynes ET (September 1968). "Prior probabilities" (PDF). IEEE Transactions on Systems Science and Cybernetics. 4 (3): 227–241. doi:10.1109/TSSC.1968.300117.
^Firth, David (1992). "Bias reduction, the Jeffreys prior and GLIM". In Fahrmeir, Ludwig; Francis, Brian; Gilchrist, Robert; Tutz, Gerhard (eds.). Advances in GLIM and Statistical Modelling. New York: Springer. pp. 91–100. doi:10.1007/978-1-4612-2952-0_15. ISBN 0-387-97873-9.
^Magis, David (2015). "A Note on Weighted Likelihood and Jeffreys Modal Estimation of Proficiency Levels in Polytomous Item Response Models". Psychometrika. 80: 200–204. doi:10.1007/s11336-013-9378-5.
In Bayesian probability, the Jeffreysprior, named after Sir Harold Jeffreys, is a non-informative prior distribution for a parameter space; its density...
probabilities, using the following priors, are such that: mean for Bayes prior > mean for Jeffreysprior > mean for Haldane prior. For s/n > 1/2 the order of...
reference priors and Jeffreyspriors are identical, even though Jeffreys has a very different rationale. Reference priors are often the objective prior of choice...
information plays a role in the derivation of non-informative prior distributions according to Jeffreys' rule. It also appears as the large-sample covariance...
Sir Harold Jeffreys, FRS (22 April 1891 – 18 March 1989) was a British geophysicist who made significant contributions to mathematics and statistics. His...
Jeffreys is a surname that may refer to the following notable people: Alec Jeffreys (born 1950), British biologist and discoverer of DNA fingerprinting...
in the 18th century by Pierre-Simon Laplace. When relying on Jeffreysprior, the prior is Beta ( α = 1 2 , β = 1 2 ) {\displaystyle \operatorname {Beta}...
{\displaystyle \ p=0.5~.} The Jeffreys interval is the Bayesian credible interval obtained when using the non-informative Jeffreysprior for the binomial proportion...
predictive posterior distribution, obtained using the non-informative Jeffreysprior 1/λ; the Conditional Normalized Maximum Likelihood (CNML) predictive...
variable τ {\displaystyle \tau \,\!} in the example. The usual priors such as the Jeffreysprior often do not work, because the posterior distribution will...
Bayesian estimator using Jeffreysprior which leads to using a dirichlet distribution, with all parameters being equal to 0.5, as a prior. The posterior will...
appears in the Lévy arcsine law, in the Erdős arcsine law, and as the Jeffreysprior for the probability of success of a Bernoulli trial. The distribution...
transformation groups as in the Jeffreysprior, and the principle of maximum entropy. More generally, one speaks of uninformative priors. Bayesian epistemology...
each probability is between 0 and 1, and they all sum to 1). Using the Jeffreysprior approach, a pseudocount of one half should be added to each possible...
)} . The prior distribution might not be easily determined; in such a case, one possibility may be to use the Jeffreysprior to obtain a prior distribution...
marginal likelihood codes. For exponential families of distributions, when Jeffreysprior is used and the parameter space is suitably restricted, these asymptotically...
prior distribution. For the group of affine transformations on the parameter space of the normal distribution, the right Haar measure is the Jeffreys...
^{2}}}-1\right)^{2}\right]} A standard choice of uninformative prior for this problem is the Jeffreysprior, p ( σ 2 ) ∝ 1 / σ 2 {\displaystyle \scriptstyle {p(\sigma...
different states and the use of the volume element as a candidate for the Jeffreysprior probability density for mixed quantum states. The Bures distance is...
was introduced by Ernst Hellinger in 1909. It is sometimes called the Jeffreys distance. To define the Hellinger distance in terms of measure theory,...
\sigma }\rightarrow p(\log(\sigma )|I)\propto 1} Which is well-known Jeffreysprior for scale parameters, which is "flat" on the log scale, although it...
which is subject to error. Later Jeffreys uses the term in his defense of the methods of Bayes and Laplace, in Jeffreys (1939). The term "Bayesian", which...
priors (for appropriate classes of regular problems) has been the quest of statistical theorists from Laplace to John Maynard Keynes, Harold Jeffreys...