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Related papers: Power laws distributions in objective priors

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Given the precision of current neutrino data, priors still impact noticeably the constraints on neutrino masses and their hierarchy. To avoid our understanding of neutrinos being driven by prior assumptions, we construct a prior that is…

Cosmology and Nongalactic Astrophysics · Physics 2018-05-02 Alan F. Heavens , Elena Sellentin

We propose a way to construct fiducial distributions for a multidimensional parameter using a step-by-step conditional procedure related to the inferential importance of the components of the parameter. For discrete models, in which the…

Statistics Theory · Mathematics 2016-12-07 Piero Veronese , Eugenio Melilli

We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution $P_0$, which may not be in the support of the prior, we show that the posterior…

Statistics Theory · Mathematics 2007-06-13 B. J. K. Kleijn , A. W. van der Vaart

We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…

Statistics Theory · Mathematics 2021-02-12 Qiyang Han

The total number of patents produced by a country (or the number of patents produced per capita) is often used as an indicator for innovation. Here we present evidence that the distribution of patents amongst applicants within many OECD…

Physics and Society · Physics 2015-06-04 D. R. J. O'Neale , S. C. Hendy

We investigate the asymptotic behavior of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution…

Methodology · Statistics 2018-03-06 Artin Armagan , David B. Dunson , Jaeyong Lee , Waheed U. Bajwa , Nate Strawn

In this note, the practical use of priors for Bayes estimators, of the two parameters of the Weibull reliability model, is discussed in a technological context. The meaning of the priors as expression of virtual data samples is analyzed.…

Statistics Theory · Mathematics 2013-10-29 Pasquale Erto , Massimiliano Giorgio

Ordinal response model is a popular and commonly used regression for ordered categorical data in a wide range of fields such as medicine and social sciences. However, it is empirically known that the existence of ``outliers'', combinations…

Methodology · Statistics 2023-05-15 Tomotaka Momozaki , Tomoyuki Nakagawa

We derive the class of normalized generalized Gamma processes from Poisson-Kingman models (Pitman, 2003) with tempered alfa-stable mixing distribution. Relying on this construction it can be shown that in Bayesian nonparametrics, results on…

Probability · Mathematics 2007-11-14 Annalisa Cerquetti

We study the properties of variational Bayes approximations for exponential family models with missing values. It is shown that the iterative algorithm for obtaining the variational Bayesian estimator converges locally to the true value…

Statistics Theory · Mathematics 2012-07-19 Bo Wang , D. Titterington

To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…

Statistical Mechanics · Physics 2008-12-02 Hari M. Gupta , Jose R. Campanha

When model uncertainty is handled by Bayesian model averaging (BMA) or Bayesian model selection (BMS), the posterior distribution possesses a desirable "oracle property" for parametric inference, if for large enough data it is nearly as…

Statistics Theory · Mathematics 2018-02-05 Wenxin Jiang , Cheng Li

The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but do not incorporate population-level heterogeneity in infection susceptibility.…

Populations and Evolution · Quantitative Biology 2023-08-04 Christopher Rose , Andrew J. Medford , C. Franklin Goldsmith , Tejs Vegge , Joshua S. Weitz , Andrew A. Peterson

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum $\gamma$-divergence estimator is well-known to work well estimation against heavy contamination. The robust Bayesian…

Methodology · Statistics 2021-02-03 Tomoyuki Nakagawa , Shintaro Hashimoto

Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper…

Digital Libraries · Computer Science 2014-02-18 Michal Brzezinski

Most of the consistency analyses of Bayesian procedures for variable selection in regression refer to pairwise consistency, that is, consistency of Bayes factors. However, variable selection in regression is carried out in a given class of…

Methodology · Statistics 2015-07-30 Elías Moreno , Javier Girón , George Casella

We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…

Applications · Statistics 2016-01-12 Francisco J. Rubio , Marc G. Genton

The notion of confidence distributions is applied to inference about the parameter in a simple autoregressive model, allowing the parameter to take the value one. This makes it possible to compare to asymptotic approximations in both the…

Methodology · Statistics 2023-03-28 Rolf Larsson

Assuming an exponential power distribution is one way to deal with outliers in regression and clustering, which can increase the robustness of the analysis. Gaussian distribution is a special case of an exponential distribution. And an…

Methodology · Statistics 2020-12-22 Xiao Chen

We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the "true" solution occurs on the boundary of the parameter space. We show that in this case Bayesian inference is consistent, and…

Statistics Theory · Mathematics 2014-10-02 Natalia A. Bochkina , Peter J. Green