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Topic: Jeffreys prior

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	Prior probability - Wikipedia, the free encyclopedia
		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 Jeffreys prior attempts to solve this problem by computing a prior which expresses the same belief no matter which metric is used.
	en.wikipedia.org /wiki/Prior_probability (1336 words)

	Encyclopedia: Prior probability (Site not responding. Last check: 2007-11-07)
		In Bayesian probability theory, a conjugate prior is a prior distribution which has the property that the posterior distribution is the same type of distribution.
		In Bayesian probability, the Jeffreys prior is a noninformative prior distribution proportional to the square root of the Fisher information: and is invariant under reparameterization of.
		The issue is particularly acute in hierarchical models; the usual priors (e.g., Jeffreys' prior) may give badly inadmissible decision rules if employed at the higher levels of the hierarchy.
	www.nationmaster.com /encyclopedia/Prior-probability (2189 words)

	KLUEDO - Jeffreys' prior is the Hausdorff measure for the Hellinger and Kullback-Leibler distances
		KLUEDO - Jeffreys' prior is the Hausdorff measure for the Hellinger and Kullback-Leibler distances
		Jeffreys' prior is the Hausdorff measure for the Hellinger and Kullback-Leibler distances
		We show that under suitable regulari ty conditions Jeffreys' prior is proportional to the k-dimensional Hausdorff measure w.r.t.
	kluedo.ub.uni-kl.de /volltexte/2000/767 (97 words)

	REFERENCE PRIOR BAYESIAN ANALYSIS FOR NORMAL MEAN PRODUCTS Magazine: Journal of the American Statistical Association, ... (Site not responding. Last check: 2007-11-07)
		The latter is compared with the uniform prior (the Jeffreys prior) in posterior inference and the optimal frequentist coverage criterion.
		Furthermore, it is shown that the reference prior is among the asymptotic optimal frequentist coverage probability priors under a transformation of the parameter space such that the parameter of interest and the nuisance parameters are orthogonal.
		The prior in (9) is the same as the prior used by Berger and Bernardo (1989), and the prior in (7) is a generalized form of (9).
	mgv.mim.edu.my /Articles/00442/9602136.Htm (3261 words)

	Priors
		These prior beliefs are needed for the variables which are at the beginning of the causal chains of the model.
		The problem of determining a prior is simplified because instead of assigning a separate prior for all variables in the set, only one prior is needed for the hidden variable.
		It is noteworthy that in models lacking hyperparameters, a combination of Jeffreys' prior and the modified MAP estimate is equal to ML estimation.
	www.cis.hut.fi /harri/thesis/valpola_thesis/node35.html (906 words)

	[No title]
		When no prior information is available, a non-informative prior such as a uniform prior, Jeffreys prior, or reference prior can be used; see (Yang and Berger, 1997) for a list of such noninformative priors.
		However, real prior information such as historical data or data from previous similar studies is often available in applied research settings where the investigator has access to previous studies measuring the same response and covariates as the current study.
		The general notion of the power prior is that it is a likelihood function raised to a positive power, where the power is between 0 and 1.
	www.stat.uconn.edu /~mhchen/LaTex/onecolumn.tex (1097 words)

	Pescara July 1-5 2002 - Information geometry and its applications (Site not responding. Last check: 2007-11-07)
		In this paper, we generalize the Jeffreys prior from the point of view of information geometry introducing a one-parameter family of prior distributions, which we named alpha-parallel priors.
		The alpha-parallel prior is defined as the parallel volume element with respect to the alpha-connection and coincides with the Jeffreys prior when alpha=0.
		Although the Jeffreys prior always exists, the existence of alpha-parallel prior with non-zero alpha is not always guaranteed.
	www.sci.unich.it /convegni/infgeo/abs/takeuchi.html (182 words)

	Abstract for Cowles Foundation Discussion Paper 1199 (Site not responding. Last check: 2007-11-07)
		Competition is fierce, and the buyer enjoys high rents, when the prior belief is biased in favor of one good and private signals are not very informative: the ex ante superior seller cannot resist the temptation to clear the market, and triggers an aggressive response by the competitor.
		The Jeffreys prior is shown to give rise to a marginal posterior density which has Cauchy-like tails similar to that exhibited by the exact finite sample distribution of the corresponding LIML estimator.
		A stronger correspondence is established in the special case of a just-identified orthonormal canonical model, where the posterior density under the Jeffreys prior is shown to have the same functional form as the density of the finite sample distribution of the LIML estimator.
	www.econ.yale.edu /cowles/P/ab/a11/a1199.htm (370 words)

	Jeffreys' Prior for Layered Neural Networks (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Abstract: In this paper, Jeffreys' prior for a neural network is discussed in the framework of the Bayesian statistics.
		Jeffreys' prior is known as a typical non-informative objective prior.
		13 Jeffreys' Prior is asymptotically least favorable under entr..
	citeseer.ist.psu.edu /53379.html (251 words)

	Interval Estimation for a Binomial Proportion, Lawrence D. Brown, T. Tony Cai, Anirban DasGupta
		Thus a uniform prior for arcsin 1/2, where is the binomial proportion, leads to Jeffreys Beta (1/2, 1/2) prior for.
		It may be worthwhile developing these priors in the presence of nuisance parameters for other discrete cases as well, for example when the parameter of interest is the difference of two binomial proportions, or the log-odds ratio in a 2 × 2 contingency table.
		The two diametrically opposite priors Beta (2, 2) (symmetric concave with maximum at 1/2 which provides the Agresti-Coull interval) andJeffreys prior Beta (1/2 1/2) (symmetric convex with minimum at 1/2) seem to be equally good for recentering.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.ss/1009213286 (2591 words)

	Citations: Jeffreys' prior is asymptotically least favorable under entropy risk - Clarke, Barron (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Jeffreys' prior is asymptotically least favorable under entropy risk.
		In the case of the mixture code, this term is a constant depending on the parameter 0 5 unless the prior is selected as Jeffreys prior (cf.
		Jeffrey' prior is asymptotically least favorable under entropy risk.
	citeseer.lcs.mit.edu /context/276593/0 (1610 words)

	JIRSS
		This paper develops default priors for Bayesian analysis that reproduce familiar frequentist and Bayesian analyses for models that are exponential or location.
		We derive the general construction of the location reparameterization that gives the natural parameter of the location model coinciding with the given model to first derivative at a data point; the derivation is in algorithmic form that is suitable for computer algebra.
		We then define a general default prior based on this location reparameterization; this gives third order agreement between frequentist p-values and Bayesian survivor values; in the vector case however, an adjustment factor is needed for component parameters that are not linear in the location parameterization.
	www.irstat.ir /Files/En/JIRSS/OldISSues/1-4.htm (403 words)

	Maximum Entropy Principle (Site not responding. Last check: 2007-11-07)
		Frequently partial prior information is available, outside of which it is desired to use a prior that is as noninformative as possible.
		For example, suppose the prior mean is specified, and among prior distributions with this mean the most noninformative distribution is sought.
		Intuitively this should result in a prior which incorporates the available prior information, but otherwise is as noninformative as possible.
	ct.radiology.uiowa.edu /~jiangm/courses/mm-cv-ip/node19.html (775 words)

	Department of Mathematics (Site not responding. Last check: 2007-11-07)
		Find a transformation $\psi=\psi(\theta)$ which is so defined in terms of $I(\thetax)$ that the Jeffreys prior $p(\psi)$ is uniform in $\psi$.
		Find the Jeffreys prior for the parameter $\alpha$ of the Maxwell distribution \[ p(x\alpha) = \sqrt{(2/\pi)}\alpha^{3/2}x^2\exp(-\half\alpha x^2) \] and find a transformation of this parameter in which the corresponding prior is uniform.
		Give an interval in which you would be 95\% sure that $\pi$ lay assuming that you used Haldane's prior and that 16 trials of an experiment with probability of success $\pi$ had resulted in 10 successes.
	www.york.ac.uk /depts/maths/exams/bayes/exam90.htm (554 words)

	Harold Jeffreys as a Statistician
		Jeffreys prior is part of the furniture of Bayesian statistics but beyond that the work of Harold Jeffreys is little known.
		Jeffreys is often described as the founder of modern British geophysics.
		Jeffreys (1933) criticised Fisher (1932) and Fisher (1933) criticised Jeffreys (1932) with a rejoinder, Jeffreys (1933a).
	www.economics.soton.ac.uk /staff/aldrich/jeffreysweb.htm (2637 words)

	Abstract Lennart Svensson (Site not responding. Last check: 2007-11-07)
		For the linear signal model, a relation between the standard Adaptive Maximum Likelihood (AML) estimator and the usage of the Jeffreys prior distribution is established.
		Moreover, a connection between the regularized version of the AML estimator and an adjustment to the Jeffreys prior is also recognized.
		To circumvent difficulties with the usage of an improper prior for the signal parameter, different versions of Intrinsic Bayes Factors are exploited.
	www.s2.chalmers.se /seminars/2004ht/Lennart_Svensson_abs.html (377 words)

	Local sensitivity of posterior expectations, Paul Gustafson
		We investigate the degree to which posterior expectations are sensitive to prior distributions, using a local method based on functional differentiation.
		We find that to maintain asymptotically sensible behaviour, it is necessary to reduce the richness of the class of prior perturbations as the dimension of the parameter space increases.
		Jeffreys' prior is characterized as the prior to which inference is least sensitive.
	projecteuclid.org /Dienst/UI/1.0/Display/euclid.aos/1033066205 (545 words)

	Nat' Academies Press, From Death to Birth: Mortality Decline and Reproductive Change (1998)
		It illustrates the evolution of perceptions for a family beginning in 1948 with a prior distribution whose mean is identical to the true survival probability (0.699), but with considerable uncertainty about 0, as evident in the 25th to 75th percentile range that stretches from 0.57 to 0.86.
		MARK R. prior distribution is quickly reduced, and even though the initial subjective mean and the true mean were selected to exactly coincide, the family's perception of child survival fails to keep pace with the empirical realities.
		Social Learning When beta-distnbuted prior beliefs about ~ are updated by reference to a sample of N external observations on child survival, this sample being generated by the binomial distnbution, the posterior distnbution for ~ is also a beta.
	www.nap.edu /books/0309058961/html/112.html (7473 words)

	KLUEDO - Shannon-Optimal Priors on iid Statistical Experiments Converge Weakly to Jeffreys Prior
		In 1979, J.M. Bernardo argued heuristically that in the case of regular product experiments his information theoretic reference prior is equal to Jeffreys' prior.
		In this context, B.S. Clarke and A.R. Barron showed in 1994, that in the same class of experiments Jeffreys' prior is asymptotically optimal in the sense of Shannon, or, in Bayesian terms, Jeffreys' prior is asymptotically least favorable under Kullback Leibler risk.
		This means that for increasing sample size Kullback Leibler least favorable priors tend to Jeffreys' prior.
	kluedo.ub.uni-kl.de /volltexte/2000/775 (165 words)

	University of Edinburgh, Economics Papers
		The reference prior algorithm (Berger and Bernardo 1992) is applied to multivariate location-scale models with any regular sampling density, where we establish the irrelevance of the usual assumption of Normal sampling if our interest is in either the location or the scale.
		On the other hand, an essentially arbitrary step in the reference prior algorithm, namely the choice of the nested sequence of sets in the parameter space is seen to play a role.
		Our results lend an additional motivation to the often used prior proportional to the inverse of the scale parameter, as it is found to be both the independence Jeffreys' prior and the reference prior under variation independence in the sequence of sets, for any choice of the sampling density.
	www.econ.ed.ac.uk /papers/Abstract-Steel10.html (172 words)

	Priors and Reference Analysis
		In the fully Bayesian framework the choice of prior is critical to the inference we perform.
		Reference priors are priors which attempt to reflect such prior ignorance.
		In cases where such null hypothesis frequentist inference for the GLM is known, the Berger-Bernardo reference priors give the same probabilities when we test the probability that a contrast is greater than zero.
	www.fmrib.ox.ac.uk /analysis/techrep/tr03mw1/tr03mw1/node7.html (304 words)

	OhioLINK ETD: WANG, GUOJUN
		The reference prior approach is used to estimate parameters in the measurement error models, including simple normal structural models, Berkson models, structural models with replicates, and the hybrid models.
		Jeffreys prior is obtained as a special case of reference priors.
		The reference priors and the FBF are derived.
	www.ohiolink.edu /etd/view.cgi?ucin1076852153 (186 words)

	Abstracts (Site not responding. Last check: 2007-11-07)
		Applications are given to characterize optimal noninformative priors in the sense of Stein (1985), to suggest the form of a high order correction to the distribution function of a sequential likelihood ratio statistic, and to provide confidence intervals for one parameter in the presence of other nuisance parameters.
		When both the parameters are of interest, it is also shown that the reference prior agrees with the prior matching the posterior and frequentist expansions based on the signed square root of log-likelihood ratio.
		The Jeffreys prior is not a second order matching prior, but the reference prior is a always a third order matching prior.
	www.stat.missouri.edu /~chong/abs/abs.html (1439 words)

	Garland Jeffreys Albums (Site not responding. Last check: 2007-11-07)
		Garland Jeffreys' prior album, the brilliant Don't Call Me Buckwheat, slipped under the public radar in America, but Jeffreys got by on a European following and critical acclaim.
		Jeffreys spent most of the time off coming to terms with his mixed-race background, and this thematically consistent disc could easily serve as a primer on the...
		A live recording on which Garland Jeffreys is backed by England's the Rumour, minus Bob Andrews, this is a fine rockin' set with a great rendition of "96 Tears" as well as his classic "Wild in the Streets." Good rockin' fun.
	www.mp3.com /Garland-Jeffreys/artists/3930/discography.html (413 words)

	1 No. 120: Christine A. Jeffreys v. Dr. Patrick H. Griffin
		In December 1991, plaintiff Christine A. Jeffreys began treatment with defendant Dr. Patrick H. Griffin, a gastroenterologist, for stomach problems and depression, for which defendant prescribed anti-depressants.
		Plaintiff had been evicted from her apartment in July 1991, and she blamed her ailments on stress caused by her landlord's supposedly oppressive conduct.
		When Niagara Mohawk moved to dismiss the action based on the PSC's prior determination and the PSC, added as a party at the trial court's behest, moved for summary judgment on the same grounds, Supreme Court granted the motions.
	www.law.cornell.edu /nyctap/I03_0125.htm (2136 words)

	PRIOR Statement
		The prior density of the variance components is, by default, a noninformative version of Jeffreys' prior (Box and Tiao 1973).
		The prior density of the fixed-effects parameters is assumed to be flat (equal to 1), and the resulting posterior is conditionally multivariate normal (conditioning on the variance component parameters) with mean ( X ' V
		specifies a noninformative reference version of Jeffreys' prior constructed using the square root of the determinant of the expected information matrix as in (1.3.92) of Box and Tiao (1973).
	support.sas.com /91doc/getDoc/statug.hlp/mixed_sect17.htm (1531 words)

	Paper Abstract (Site not responding. Last check: 2007-11-07)
		It is thus necessary to determine an objective (or default) prior distribution for the unknown mean and covariance parameters of the random field.
		Next, the reference prior for the model is developed, and is shown to yield a proper posterior distribution.
		A further attractive property of the reference prior is that it can be used directly for computation of Bayes factors or posterior probabilities of hypotheses to compare different correlation functions, even though the reference prior is improper.
	www.isds.duke.edu /~berger/papers/00-12.html (201 words)

	Bayesian prediction with approximate frequentist validity, Gauri Sankar Datta, Rahul Mukerjee, Malay Ghosh, Trevor J. ...
		We characterize priors which asymptotically match the posterior coverage probability of a Bayesian prediction region with the corresponding frequentist coverage probability.
		The resulting priors are shown to be invariant under reparameterization.
		It is further shown that, for any given prior, it may be possible to choose an interval whose Bayesian predictive and frequentist coverage probabilities are asymptotically matched.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aos/1015957400 (465 words)

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