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## Bayesian estimation of generalized exponential distribution under noninformative priors

Moala, Fernando Antonio; Achcar, Jorge Alberto; Damasceno Tomazella, Vera Lucia; Stern, JM; Lauretto, MD; Polpo, A; Diniz, MA
Fonte: Amer Inst Physics Publicador: Amer Inst Physics
Tipo: Conferência ou Objeto de Conferência Formato: 230-242
ENG
Relevância na Pesquisa
47.08%
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.

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

Moala, Fernando A.; Garcia, Lívia M.
Tipo: Artigo de Revista Científica Formato: 282-291
ENG
Relevância na Pesquisa
26.56%
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.

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

Moala, Fernando Antonio; Ramos, Pedro Luiz; Achcar, Jorge Alberto
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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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.

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

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

Hornik, Kurt; Grün, Bettina
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Publicado em /05/2013 EN
Relevância na Pesquisa
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.

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

Bousquet, Nicolas
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
37.02%
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

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

Northrop, Paul J.; Attalides, Nicolas
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

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

Fouskakis, Dimitris; Ntzoufras, Ioannis
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.

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

D'Agostini, G.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.08%
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

## On the Jeffreys-Lindley's paradox

Robert, Christian
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.56%
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)

## Objective priors for the bivariate normal model

Berger, James O.; Sun, Dongchu
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.75%
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)

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

Vallejos, Catalina A.; Steel, Mark F. J.
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

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

Honda, Junya; Takemura, Akimichi
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.63%
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.

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

Choi, Jaehyung; Mullhaupt, Andrew P.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.75%
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

## Shrinkage priors for Bayesian prediction

Komaki, Fumiyasu
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.75%
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)

## Default priors for Gaussian processes

Paulo, Rui
Tipo: Artigo de Revista Científica
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)

## Jeffreys priors for mixture estimation

Grazian, Clara; Robert, Christian
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.11%
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.

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

Bayarri, M. J.; García-Donato, G.
Tipo: Artigo de Revista Científica
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.

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

Burghaus, Ina; Dette, Holger
Tipo: Artigo de Revista Científica