Reschenhofer, Erhard · The Egyptian Statistical Journal/The Egyptian Statistical Journal · 2000
In this article, I investigate two classes of noninformative priors: the reference priors of Berger and Bernardo and the reverse reference priors attributed to J.K. Ghosh. Datta and Ghosh (1995) gave a simple condition under which reference priors agree with reverse reference priors. They also gave several examples showing agreement or disagreement between the two priors. I derive the reference priors and reverse reference priors for several reparametrization of one of these examples, examine the invariance properties of the different parametrizations, and observe an interesting relationship between priors and invariance properties.
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B. Clarke, A. Yuan · 2000
Suppose X 1 ; : : : ; X n are IID p(j; ) where (; ) 2 IR d is distributed according to the prior density w(). For estimators S n = S(X n ) and T n = T (X n ) assumed to be consistent for some function of and asymptotically normal we examine the conditional Shannon mutual information (CSMI) between and T n given \t and S n , I(; T n j\t; S n ). It is seen there are several important special cases of this CSMI. We establish an asymptotic formula for it and identify the resulting noninformative reference prior. As a consequence, we develop the notion of data dependent priors and a calibration for how close an estimator is to sufficiency.
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Pierini, Maurizio, Prosper, Harrison, Sekmen, Sezen et al. · CERN Document Server (European Organization for Nuclear Research) · 2011
We describe the application of model inference based on reference priors to two concrete examples in high energy physics: the determination of the CKM matrix parameters rhobar and etabar and the determination of the parameters m_0 and m_1/2 in a simplified version of the CMSSM SUSY model. We show how a 1-dimensional reference posterior can be mapped to the n-dimensional (n-D) parameter space of the given class of models, under a minimal set of conditions on the n-D function. This reference-based function can be used as a prior for the next iteration of inference, using Bayes' theorem recursively.
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Bishop, N, Jarne Ornia, D, Dyer, JD et al. · Oxford University Research Archive (ORA) (University of Oxford) · 2025
Simulation modeling offers a flexible approach to constructing high-fidelity synthetic representations of complex real-world systems. However, the increased complexity of such models introduces additional complications, for example when carrying out statistical inference procedures. This has motivated a large and growing literature on likelihood-free or simulation-based inference methods, which approximate (e.g., Bayesian) inference without assuming access to the simulator’s intractable likelihood function. A hitherto neglected problem in the simulation-based Bayesian inference literature is the challenge of constructing uninformative reference priors for complex simulation models. Such priors maximise an expected Kullback-Leibler distance from the prior to the posterior, thereby influencing posterior inferences minimally and enabling an “objective” approach to Bayesian inference that do not necessitate the incorporation of strong subjective prior beliefs. In this paper, we propose and test a selection of likelihood-free methods for learning reference priors for simulation models, using variational approximations to these priors and a variety of mutual information estimators. Our experiments demonstrate that good approximations to reference priors for simulation models are in this way attainable, providing a first step towards the development of likelihood-free objective Bayesian inference procedures.
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WORLD SCIENTIFIC eBooks · 2024
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Pierini, Maurizio · CERN Document Server (European Organization for Nuclear Research) · 2011
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Demortier, Luc, Jain, Supriya, Prosper, Harrison B. · arXiv (Cornell University) · 2010
Bayesian inferences in high energy physics often use uniform prior distributions for parameters about which little or no information is available before data are collected. The resulting posterior distributions are therefore sensitive to the choice of parametrization for the problem and may even be improper if this choice is not carefully considered. Here we describe an extensively tested methodology, known as reference analysis, which allows one to construct parametrization-invariant priors that embody the notion of minimal informativeness in a mathematically well-defined sense. We apply this methodology to general cross section measurements and show that it yields sensible results. A recent measurement of the single top quark cross section illustrates the relevant techniques in a realistic situation.
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Bertrand Clarke, Subhashis Ghosal · 2009
In this article, we study asymptotic normality of the posterior distribution of the natural parameter in an exponential family based on independent and identically distributed (i.i.d.) data, that is, in terms of expected Kullback-Leibler divergence, when the number of parameters p is increasing with the sample size n. We use this to generate an asymptotic expansion of the Shannon mutual information, p is allowed to increase with n. The leading term, dependent on the prior in the asymptotic expansion, can be optimized to give Jeffreys’ prior as the reference prior in the absence of nuisance parameters. In two examples, we determine the rates at which p = pn can be allowed to increase while still retaining the reference prior.
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Subhashis Ghosal · Test · 1997
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James O. Berger, José M. Bernardo · 1992
Abstract The paper begins with a general, though idiosyncratic, discussion of noninformative priors. This provides the background for motivating the recent and ongoing elaborations of the reference prior method for developing noninformative priors, a method initiated in Bernardo (1979). Included in this description of the reference prior method is a new condition that has not previously appeared. Motivation for this new condition is found, in part, in the Fraser, Monette, Ng (1985) example. Extensive discussion of the motivation for reference priors and the specific steps in the algorithm are given, with reference to new examples where appropriate. Also, technical issues in implementing the algorithm are discussed.
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Shemyakin, Arkady · UST Research Online (University of St. Thomas - Minnesota) · 2010
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Alban Foulonneau, Pierre Charbonnier, Fabrice Heitz · International Journal of Computer Vision · 2008
Cited by 49Open access
Fernandez Llana, MDC, Steel, M · Bristol Research (University of Bristol) · 1998
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C. Steel, Carmen Fern, Mark F. J. Steel · 1998
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Likun Zhang, Benjamin A. Shaby · Statistica Sinica · 2022
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Chetkar Jha, Dongchu Sun · Bayesian Analysis · 2022
Reference prior algorithms are primarily available for models that have asymptotic posterior normality (i.e., regular case), barring for a specific class of models whose posteriors are not asymptotically normal (i.e., non-regular case). In particular, the current reference prior methodology is contingent on models belonging to regular or non-regular cases. This highlights that the existing reference prior theory lacks a unified approach. A partial breakthrough in unifying the reference prior theory came with Berger et al. (2009) deriving an explicit form of reference prior for single group models (i.e., models with a scalar parameter or models that have all the parameters on equal footing or importance). Unfortunately, their approach does not generalize to multi-group models (i.e., models that have parameters’ subsets ordered according to their importance). In this paper, we show that their main result can be extended with modifications to multi-group models. As a consequence, we obtain a general scheme for deriving conditional reference priors. We also prove that the invariance property of reference priors under particular transformations hold for both regular and non-regular cases. We show the usefulness of our approach by computing reference priors for models that have no known reference priors.
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Carmen Fernández, Mark F. J. Steel · Statistics & Probability Letters · 1999
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Kostas Triantafyllopoulos · Communication in Statistics- Theory and Methods · 2008
We develop reference analysis for matrix-variate dynamic models with unknown observation covariance matrices. Bayesian algorithms for forecasting, estimation, and filtering are derived. This work extends the existing theory of reference analysis for univariate dynamic linear models, and thus it proposes a solution to the specification of the prior distributions for a very wide class of time series models. Subclasses of our models include the widely used multivariate and matrix-variate regression models.
Cited by 1
Tin-yau Kwok, Dit-Yan Yeung · 2007
Motivated by the principle of maximum entropy, the Laplace prior has been introduced in the Bayesian inference approach to training feedforward neural networks as the prior distribution for network weights. In this paper, we examine in detail the arguments supporting the Laplace prior and argue that network weights, being continuous quantities with no obvious upper bound, complicate the application of the maximum entropy principle. On the other hand, we motivate the use of the Gaussian prior as reference prior in neural networks, basing on the assumptions of exchangeability and spherical symmetry. 1 Introduction The Bayesian approach [1, 2, 3] is attractive in being logically consistent, simple and flexible. Recently, various researchers [4, 5, 6, 7] have incorporated Bayesian methods into the learning of feedforward neural networks. Compared with the traditional approach, it provides a rigorous framework and enables objective comparison between solutions using alternative network ar...
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Steel, M.F.J., Fernández, C. · Research portal (Tilburg University) · 1998
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