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## Bayesian estimation of generalized exponential distribution under noninformative priors

Fonte: Amer Inst Physics
Publicador: Amer Inst Physics

Tipo: Conferência ou Objeto de Conferência
Formato: 230-242

ENG

Relevância na Pesquisa

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The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional non-informative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods.

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## A bayesian analysis for the parameters of the exponential-logarithmic distribution

Fonte: Universidade Estadual Paulista
Publicador: Universidade Estadual Paulista

Tipo: Artigo de Revista Científica
Formato: 282-291

ENG

Relevância na Pesquisa

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#Bayesian#exponential-logarithmic distribution#Jeffreys#MCMC#noninformative prior#posterior#Non-informative prior#Maximum likelihood estimation#Bayesian networks

The exponential-logarithmic is a new lifetime distribution with decreasing failure rate and interesting applications in the biological and engineering sciences. Thus, a Bayesian analysis of the parameters would be desirable. Bayesian estimation requires the selection of prior distributions for all parameters of the model. In this case, researchers usually seek to choose a prior that has little information on the parameters, allowing the data to be very informative relative to the prior information. Assuming some noninformative prior distributions, we present a Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. Jeffreys prior is derived for the parameters of exponential-logarithmic distribution and compared with other common priors such as beta, gamma, and uniform distributions. In this article, we show through a simulation study that the maximum likelihood estimate may not exist except under restrictive conditions. In addition, the posterior density is sometimes bimodal when an improper prior density is used. © 2013 Copyright Taylor and Francis Group, LLC.

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## Bayesian inference for two-parameter gamma distribution assuming different noninformative priors

Fonte: Univ Nac Colombia, Dept Estadistica
Publicador: Univ Nac Colombia, Dept Estadistica

Tipo: Artigo de Revista Científica
Formato: 321-338

ENG

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#Gamma distribution#noninformative prior#copula#conjugate#Jeffreys prior#reference#MDIP#orthogonal#MCMC

In this paper distinct prior distributions are derived in a Bayesian inference of the two-parameters Gamma distribution. Noniformative priors, such as Jeffreys, reference, MDIP, Tibshirani and an innovative prior based on the copula approach are investigated. We show that the maximal data information prior provides in an improper posterior density and that the different choices of the parameter of interest lead to different reference priors in this case. Based on the simulated data sets, the Bayesian estimates and credible intervals for the unknown parameters are computed and the performance of the prior distributions are evaluated. The Bayesian analysis is conducted using the Markov Chain Monte Carlo (MCMC) methods to generate samples from the posterior distributions under the above priors.

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## Inferência bayesiana em modelos de regressão beta e beta inflacionados; Bayesian inference in beta and inflated beta regression models

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 04/07/2013
PT

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#Regressão beta inflacionada#Inferência bayesiana#Métodos MCMC#Jeffreys#Priori de#Inflated beta regression#Bayesian inference#MCMC methods#Jeffreys prior

No presente trabalho desenvolvemos ferramentas de inferência bayesiana para modelos de regressão beta e beta inflacionados, em relação à estimação paramétrica e diagnóstico. Trabalhamos com modelos de regressão beta não inflacionados, inflacionados em zero ou um e inflacionados em zero e um. Devido à impossibilidade de obtenção analítica das posteriores de interesse, tais ferramentas foram desenvolvidas através de algoritmos MCMC. Para os parâmetros da estrutura de regressão e para o parâmetro de precisão exploramos a utilização de prioris comumente empregadas em modelos de regressão, bem como prioris de Jeffreys e de Jeffreys sob independência. Para os parâmetros das componentes discretas, consideramos prioris conjugadas. Realizamos diversos estudos de simulação considerando algumas situações de interesse prático com o intuito de comparar as estimativas bayesianas com as frequentistas e também de estudar a sensibilidade dos modelos _a escolha de prioris. Um conjunto de dados da área psicométrica foi analisado para ilustrar o potencial do ferramental desenvolvido. Os resultados indicaram que há ganho ao se considerar modelos que contemplam as observações inflacionadas ao invés de transformá-las a fim de utilizar modelos não inflacionados.; In the present work we developed Bayesian tools...

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## On conjugate families and Jeffreys priors for von Mises–Fisher distributions

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

Publicado em /05/2013
EN

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36.9%

This paper discusses characteristics of standard conjugate priors and their induced posteriors in Bayesian inference for von Mises–Fisher distributions, using either the canonical natural exponential family or the more commonly employed polar coordinate parameterizations. We analyze when standard conjugate priors as well as posteriors are proper, and investigate the Jeffreys prior for the von Mises–Fisher family. Finally, we characterize the proper distributions in the standard conjugate family of the (matrix-valued) von Mises–Fisher distributions on Stiefel manifolds.

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## Reference priors of nuisance parameters in Bayesian sequential population analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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Prior distributions elicited for modelling the natural fluctuations or the
uncertainty on parameters of Bayesian fishery population models, can be chosen
among a vast range of statistical laws. Since the statistical framework is
defined by observational processes, observational parameters enter into the
estimation and must be considered random, similarly to parameters or states of
interest like population levels or real catches. The former are thus perceived
as nuisance parameters whose values are intrinsically linked to the considered
experiment, which also require noninformative priors. In fishery research
Jeffreys methodology has been presented by Millar (2002) as a practical way to
elicit such priors. However they can present wrong properties in multiparameter
contexts. Therefore we suggest to use the elicitation method proposed by Berger
and Bernardo to avoid paradoxical results raised by Jeffreys priors. These
benchmark priors are derived here in the framework of sequential population
analysis.; Comment: This paper has been withdrawn by the author. 8 pages (short
communication) : this paper is currently submitted and should not be cited

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## Posterior propriety in Bayesian extreme value analyses using reference priors

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

27.02%

The Generalized Pareto (GP) and Generalized extreme value (GEV) distributions
play an important role in extreme value analyses, as models for threshold
excesses and block maxima respectively. For each of these distributions we
consider Bayesian inference using "reference" prior distributions (in the
general sense of priors constructed using formal rules) for the model
parameters, specifically a Jeffreys prior, the maximal data information (MDI)
prior and independent uniform priors on separate model parameters. We
investigate the important issue of whether these improper priors lead to proper
posterior distributions. We show that, in the GP and GEV cases, the MDI prior,
unless modified, never yields a proper posterior and that in the GEV case this
also applies to the Jeffreys prior. We also show that a sample size of three
(four) is sufficient for independent uniform priors to yield a proper posterior
distribution in the GP (GEV) case.; Comment: 20 pages, 2 figures; typo corrected on page 5 (line -2, Euler's
constant corrected to approx. 0.57722). The final publication is available at
http://www3.stat.sinica.edu.tw/preprint/SS-14-034_preprint.pdf or
http://dx.doi.org/10.5705/ss.2014.034

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## Limiting behavior of the Jeffreys Power-Expected-Posterior Bayes Factor in Gaussian Linear Models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

27.02%

Expected-posterior priors (EPP) have been proved to be extremely useful for
testing hypothesis on the regression coefficients of normal linear models. One
of the advantages of using EPPs is that impropriety of baseline priors causes
no indeterminacy. However, in regression problems, they based on one or more
\textit{training samples}, that could influence the resulting posterior
distribution. The power-expected-posterior priors are minimally-informative
priors that diminishing the effect of training samples on the EPP approach, by
combining ideas from the power-prior and unit-information-prior methodologies.
In this paper we show the consistency of the Bayes factors when using the
power-expected-posterior priors, with the independence Jeffreys (or reference)
prior as a baseline, for normal linear models under very mild conditions on the
design matrix.

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## Jeffreys priors versus experienced physicist priors - arguments against objective Bayesian theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/11/1998

Relevância na Pesquisa

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I review the problem of the choice of the priors from the point of view of a
physicist interested in measuring a physical quantity, and I try to show that
the reference priors often recommended for the purpose (Jeffreys priors) do not
fit to the problem. Although it may seem surprising, it is easier for an
``experienced physicist'' to accept subjective priors, or even purely
subjective elicitation of probabilities, without explicit use of the Bayes'
theorem. The problem of the use of reference priors is set in the more general
context of ``Bayesian dogmatism'', which could really harm Bayesianism.; Comment: 9 pages, LateX, Contributed paper to the "6th Valencia International
Meeting on Bayesian Statistics", Alcossebre (Spain), May 30th - June 4th,
1998

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## On the Jeffreys-Lindley's paradox

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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This paper discusses the dual interpretation of the Jeffreys--Lindley's
paradox associated with Bayesian posterior probabilities and Bayes factors,
both as a differentiation between frequentist and Bayesian statistics and as a
pointer to the difficulty of using improper priors while testing. We stress the
considerable impact of this paradox on the foundations of both classical and
Bayesian statistics. While assessing existing resolutions of the paradox, we
focus on a critical viewpoint of the paradox discussed by Spanos (2013) in
Philosophy of Science.; Comment: 15 pages (second revision)

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## Objective priors for the bivariate normal model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/04/2008

Relevância na Pesquisa

26.75%

#Mathematics - Statistics Theory#62F10, 62F15, 62F25 (Primary) 62A01, 62E15, 62H10, 62H20 (Secondary)

Study of the bivariate normal distribution raises the full range of issues
involving objective Bayesian inference, including the different types of
objective priors (e.g., Jeffreys, invariant, reference, matching), the
different modes of inference (e.g., Bayesian, frequentist, fiducial) and the
criteria involved in deciding on optimal objective priors (e.g., ease of
computation, frequentist performance, marginalization paradoxes). Summary
recommendations as to optimal objective priors are made for a variety of
inferences involving the bivariate normal distribution. In the course of the
investigation, a variety of surprising results were found, including the
availability of objective priors that yield exact frequentist inferences for
many functions of the bivariate normal parameters, including the correlation
coefficient.; Comment: Published in at http://dx.doi.org/10.1214/07-AOS501 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org)

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## On posterior propriety for the Student-$t$ linear regression model under Jeffreys priors

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

36.92%

Regression models with fat-tailed error terms are an increasingly popular
choice to obtain more robust inference to the presence of outlying
observations. This article focuses on Bayesian inference for the Student-$t$
linear regression model under objective priors that are based on the Jeffreys
rule. Posterior propriety results presented in Fonseca et al. (2008) are
revisited and corrected. In particular, it is shown that the standard
Jeffreys-rule prior precludes the existence of a proper posterior distribution.; Comment: minor editorial changes in this version

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## Optimality of Thompson Sampling for Gaussian Bandits Depends on Priors

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/11/2013

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In stochastic bandit problems, a Bayesian policy called Thompson sampling
(TS) has recently attracted much attention for its excellent empirical
performance. However, the theoretical analysis of this policy is difficult and
its asymptotic optimality is only proved for one-parameter models. In this
paper we discuss the optimality of TS for the model of normal distributions
with unknown means and variances as one of the most fundamental example of
multiparameter models. First we prove that the expected regret of TS with the
uniform prior achieves the theoretical bound, which is the first result to show
that the asymptotic bound is achievable for the normal distribution model. Next
we prove that TS with Jeffreys prior and reference prior cannot achieve the
theoretical bound. Therefore the choice of priors is important for TS and
non-informative priors are sometimes risky in cases of multiparameter models.

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## Geometric shrinkage priors for K\"ahlerian signal filters

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

26.75%

#Mathematics - Statistics Theory#Computer Science - Information Theory#Mathematics - Differential Geometry

We construct geometric shrinkage priors for K\"ahlerian signal filters. Based
on the characteristics of K\"ahler manifolds, an efficient and robust algorithm
for finding superharmonic priors which outperform the Jeffreys prior is
introduced. Several ans\"atze for the Bayesian predictive priors are also
suggested. In particular, the ans\"atze related to K\"ahler potential are
geometrically intrinsic priors to the information manifold of which the
geometry is derived from the potential. The implication of the algorithm to
time series models is also provided.; Comment: 10 pages, published version

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## Shrinkage priors for Bayesian prediction

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/07/2006

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We investigate shrinkage priors for constructing Bayesian predictive
distributions. It is shown that there exist shrinkage predictive distributions
asymptotically dominating Bayesian predictive distributions based on the
Jeffreys prior or other vague priors if the model manifold satisfies some
differential geometric conditions. Kullback--Leibler divergence from the true
distribution to a predictive distribution is adopted as a loss function.
Conformal transformations of model manifolds corresponding to vague priors are
introduced. We show several examples where shrinkage predictive distributions
dominate Bayesian predictive distributions based on vague priors.; Comment: Published at http://dx.doi.org/10.1214/009053606000000010 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## Default priors for Gaussian processes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/05/2005

Relevância na Pesquisa

26.9%

Motivated by the statistical evaluation of complex computer models, we deal
with the issue of objective prior specification for the parameters of Gaussian
processes. In particular, we derive the Jeffreys-rule, independence Jeffreys
and reference priors for this situation, and prove that the resulting posterior
distributions are proper under a quite general set of conditions. A proper flat
prior strategy, based on maximum likelihood estimates, is also considered, and
all priors are then compared on the grounds of the frequentist properties of
the ensuing Bayesian procedures. Computational issues are also addressed in the
paper, and we illustrate the proposed solutions by means of an example taken
from the field of complex computer model validation.; Comment: Published at http://dx.doi.org/10.1214/009053604000001264 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## Jeffreys priors for mixture estimation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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While Jeffreys priors usually are well-defined for the parameters of mixtures
of distributions, they are not available in closed form. Furthermore, they
often are improper priors. Hence, they have never been used to draw inference
on the mixture parameters. We study in this paper the implementation and the
properties of Jeffreys priors in several mixture settings, show that the
associated posterior distributions most often are improper, and then propose a
noninformative alternative for the analysis of mixtures.

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## Generalization of Jeffreys' divergence based priors for Bayesian hypothesis testing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/01/2008

Relevância na Pesquisa

26.81%

In this paper we introduce objective proper prior distributions for
hypothesis testing and model selection based on measures of divergence between
the competing models; we call them divergence based (DB) priors. DB priors have
simple forms and desirable properties, like information (finite sample)
consistency; often, they are similar to other existing proposals like the
intrinsic priors; moreover, in normal linear models scenarios, they exactly
reproduce Jeffreys-Zellner-Siow priors. Most importantly, in challenging
scenarios such as irregular models and mixture models, the DB priors are well
defined and very reasonable, while alternative proposals are not. We derive
approximations to the DB priors as well as MCMC and asymptotic expressions for
the associated Bayes factors.

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## Optimal designs for nonlinear regression models with respect to non-informative priors

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/11/2013

Relevância na Pesquisa

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In nonlinear regression models the Fisher information depends on the
parameters of the model. Consequently, optimal designs maximizing some
functional of the information matrix cannot be implemented directly but require
some preliminary knowledge about the unknown parameters. Bayesian optimality
criteria provide an attractive solution to this problem. These criteria depend
sensitively on a reasonable specification of a prior distribution for the model
parameters which might not be available in all applications. In this paper we
investigate Bayesian optimality criteria with non-informative prior dis-
tributions. In particular, we study the Jeffreys and the Berger-Bernardo prior
for which the corresponding optimality criteria are not necessarily concave.
Several examples are investigated where optimal designs with respect to the new
criteria are calculated and compared to Bayesian optimal designs based on a
uniform and a functional uniform prior.; Comment: Keywords: optimal design; Bayesian optimality criteria;
non-informative prior; Jeffreys prior; reference prior; polynomial
regression; canonical moments; heteroscedasticity Pages: 21 Figures: 3

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## Approximation of improper prior by vague priors

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/11/2013

Relevância na Pesquisa

37.02%

We propose a convergence mode for prior distributions which allows a sequence
of probability measures to have an improper limiting measure. We define a
sequence of vague priors as a sequence of probability measures that converges
to a non-informative prior. We consider some cases where vague priors have
necessarily large variances and other cases where they have not. We give some
constructions of vague priors that approximate the Haar measures or the
Jeffreys priors. Then, we study the consequences of the convergence of prior
distributions on the posterior analysis. We also revisit the Jeffreys-Lindley
paradox.; Comment: 30 pages

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