Journal articles: 'Jeffreys prior'

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Poirier, Dale. "Jeffreys' prior for logit models." Journal of Econometrics 63, no. 2 (August 1994): 327–39. http://dx.doi.org/10.1016/0304-4076(93)01556-2.

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Millar, Russell B. "Reference priors for Bayesian fisheries models." Canadian Journal of Fisheries and Aquatic Sciences 59, no. 9 (September 1, 2002): 1492–502. http://dx.doi.org/10.1139/f02-108.

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Bayesian models require the specification of prior distributions for all unknown parameters, and this formal utilization of prior knowledge (if any) can be used to great advantage in some fisheries. However, regardless of whether prior knowledge about model parameters is available, specification of prior distributions is seldom unequivocal. This work addresses the problem of specifying default priors for several common fisheries models. To maintain consistency of terminology with the statistical literature, such priors are herein called reference priors to recognize that they can be interpreted as providing a sensible reference point against which the implications of alternative priors can be compared. Here, the Jeffreys' prior is demonstrated for the Ricker and BevertonHolt stockrecruit curves, von Bertalanffy growth curve, Schaefer surplus production model, and sequential population analysis. The Jeffreys' priors for relevant derived parameters are demonstrated, including the steepness parameter of the BevertonHolt stockrecruit curve. The sequential population analysis example is used to show that the Jeffreys' prior should not be automatically accepted as a reference prior in all modelsthis needs to be decided on a case-by-case basis.

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Zivot, Eric. "A Bayesian Analysis Of The Unit Root Hypothesis Within An Unobserved Components Model." Econometric Theory 10, no. 3-4 (August 1994): 552–78. http://dx.doi.org/10.1017/s0266466600008665.

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In this paper we extend some of Phillips's [4] results to nonlinear unobserved components models and develop a posterior odds ratio test of the unit root hypothesis based on flat and Jeffreys priors. In contrast to the analysis presented by Schotman and van Dijk [9], we utilize a nondegenerate structural representation of the components model that allows us to determine well-behaved Jeffreys priors, posterior densities under flat priors and Jeffreys priors, and posterior odds ratios for the unit root hypothesis without a proper prior for the level parameter. The analysis highlights the importance of the treatment of initial values for inference concerning stationarity and unit roots.

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Journal, Baghdad Science. "Comparison of Maximum Likelihood and some Bayes Estimators for Maxwell Distribution based on Non-informative Priors." Baghdad Science Journal 10, no. 2 (June 2, 2013): 480–88. http://dx.doi.org/10.21123/bsj.10.2.480-488.

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In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes estimators of the shape parameter of the Maxwell distribution decreases with the increase of Jeffreys prior constants. The results also show that values of Bayes estimators are almost close to the maximum likelihood estimator when the Jeffreys prior constants are small, yet they are identical in some certain cases. Comparison with respect to loss functions show that Bayes estimators under the modified squared error loss function has greater MSE than the squared error loss function especially with the increase of r.

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Rainey, Carlisle. "Dealing with Separation in Logistic Regression Models." Political Analysis 24, no. 3 (2016): 339–55. http://dx.doi.org/10.1093/pan/mpw014.

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When facing small numbers of observations or rare events, political scientists often encounter separation, in which explanatory variables perfectly predict binary events or nonevents. In this situation, maximum likelihood provides implausible estimates and the researcher might want incorporate some form of prior information into the model. The most sophisticated research uses Jeffreys’ invariant prior to stabilize the estimates. While Jeffreys’ prior has the advantage of being automatic, I show that it often provides too much prior information, producing smaller point estimates and narrower confidence intervals than even highly skeptical priors. To help researchers assess the amount of information injected by the prior distribution, I introduce the concept of a partial prior distribution and develop the tools required to compute the partial prior distribution of quantities of interest, estimate the subsequent model, and summarize the results.

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Khooriphan, Wansiri, Sa-Aat Niwitpong, and Suparat Niwitpong. "Confidence Intervals for the Ratio of Variances of Delta-Gamma Distributions with Applications." Axioms 11, no. 12 (November 30, 2022): 689. http://dx.doi.org/10.3390/axioms11120689.

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Since rainfall data often contain zero observations, the ratio of the variances of delta-gamma distributions can be used to compare the rainfall dispersion between two rainfall datasets. To this end, we constructed the confidence interval for the ratio of the variances of two delta-gamma distributions by using the fiducial quantity method, Bayesian credible intervals based on the Jeffreys, uniform, or normal-gamma-beta priors, and highest posterior density (HPD) intervals based on the Jeffreys, uniform, or normal-gamma-beta priors. The performances of the proposed confidence interval methods were evaluated in terms of their coverage probabilities and average lengths via Monte Carlo simulation. Our findings show that the HPD intervals based on Jeffreys prior and the normal-gamma-beta prior are both suitable for datasets with a small and large probability of containing zeros, respectively. Rainfall data from Phrae province, Thailand, are used to illustrate the practicability of the proposed methods with real data.

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Jiang, Ruichao, Javad Tavakoli, and Yiqiang Zhao. "Weyl Prior and Bayesian Statistics." Entropy 22, no. 4 (April 20, 2020): 467. http://dx.doi.org/10.3390/e22040467.

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When using Bayesian inference, one needs to choose a prior distribution for parameters. The well-known Jeffreys prior is based on the Riemann metric tensor on a statistical manifold. Takeuchi and Amari defined the α -parallel prior, which generalized the Jeffreys prior by exploiting a higher-order geometric object, known as a Chentsov–Amari tensor. In this paper, we propose a new prior based on the Weyl structure on a statistical manifold. It turns out that our prior is a special case of the α -parallel prior with the parameter α equaling − n , where n is the dimension of the underlying statistical manifold and the minus sign is a result of conventions used in the definition of α -connections. This makes the choice for the parameter α more canonical. We calculated the Weyl prior for univariate Gaussian and multivariate Gaussian distribution. The Weyl prior of the univariate Gaussian turns out to be the uniform prior.

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D’Andrea, Amanda M. E., Vera L. D. Tomazella, Hassan M. Aljohani, Pedro L. Ramos, Marco P. Almeida, Francisco Louzada, Bruna A. W. Verssani, Amanda B. Gazon, and Ahmed Z. Afify. "Objective bayesian analysis for multiple repairable systems." PLOS ONE 16, no. 11 (November 23, 2021): e0258581. http://dx.doi.org/10.1371/journal.pone.0258581.

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This article focus on the analysis of the reliability of multiple identical systems that can have multiple failures over time. A repairable system is defined as a system that can be restored to operating state in the event of a failure. This work under minimal repair, it is assumed that the failure has a power law intensity and the Bayesian approach is used to estimate the unknown parameters. The Bayesian estimators are obtained using two objective priors know as Jeffreys and reference priors. We proved that obtained reference prior is also a matching prior for both parameters, i.e., the credibility intervals have accurate frequentist coverage, while the Jeffreys prior returns unbiased estimates for the parameters. To illustrate the applicability of our Bayesian estimators, a new data set related to the failures of Brazilian sugar cane harvesters is considered.

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Uhlig, Harald. "On Jeffreys Prior when Using the Exact Likelihood Function." Econometric Theory 10, no. 3-4 (August 1994): 633–44. http://dx.doi.org/10.1017/s0266466600008707.

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In this paper, we calculate Jeffreys prior for an AR(1) process with and without a constant and a time trend when using the exact likelihood function. We show how this prior can be calculated for the explosive region, even though the unconditional variance of the process is infinite. The calculations lend additional support to the Schotman-van Dijk [6] procedure for restricting the location and the variance of the time trend coefficient. The results show that flat priors are reasonable for the nonexplosive region in an AR(1) without a constant and a time trend where the variance is known and the initial observation is zero, i.e., for the special case studied by Sims and Uhlig [7]. Differences to a flat prior analysis remain in particular for nonzero initial observations, however. For the explosive region, the unconditional prior diverges as the root diverges, supporting findings by Phillips [4]. This paper thus provides a useful perspective as well as some reconciliation for the different stands taken in the literature about priors and Bayesian inference for potentially nonstationary time series.

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Kwek, L. C., C. H. Oh, and Xiang-Bin Wang. "Quantum Jeffreys prior for displaced squeezed thermal states." Journal of Physics A: Mathematical and General 32, no. 37 (September 6, 1999): 6613–18. http://dx.doi.org/10.1088/0305-4470/32/37/310.

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Kaur, Kamaljit, Sangeeta Arora, and Kalpana K. Mahajan. "Bayesian Estimation of Inequality and Poverty Indices in Case of Pareto Distribution Using Different Priors under LINEX Loss Function." Advances in Statistics 2015 (January 29, 2015): 1–10. http://dx.doi.org/10.1155/2015/964824.

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Bayesian estimators of Gini index and a Poverty measure are obtained in case of Pareto distribution under censored and complete setup. The said estimators are obtained using two noninformative priors, namely, uniform prior and Jeffreys’ prior, and one conjugate prior under the assumption of Linear Exponential (LINEX) loss function. Using simulation techniques, the relative efficiency of proposed estimators using different priors and loss functions is obtained. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under LINEX loss function.

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Guure, Chris Bambey, Noor Akma Ibrahim, and Al Omari Mohammed Ahmed. "Bayesian Estimation of Two-Parameter Weibull Distribution Using Extension of Jeffreys' Prior Information with Three Loss Functions." Mathematical Problems in Engineering 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/589640.

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The Weibull distribution has been observed as one of the most useful distribution, for modelling and analysing lifetime data in engineering, biology, and others. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. Recently, much attention has been given to the Bayesian estimation approach for parameters estimation which is in contention with other estimation methods. In this paper, we examine the performance of maximum likelihood estimator and Bayesian estimator using extension of Jeffreys prior information with three loss functions, namely, the linear exponential loss, general entropy loss, and the square error loss function for estimating the two-parameter Weibull failure time distribution. These methods are compared using mean square error through simulation study with varying sample sizes. The results show that Bayesian estimator using extension of Jeffreys' prior under linear exponential loss function in most cases gives the smallest mean square error and absolute bias for both the scale parameterαand the shape parameterβfor the given values of extension of Jeffreys' prior.

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Fonseca, Thais C. O., Vinicius S. Cerqueira, Helio S. Migon, and Christian A. C. Torres. "Evaluating the performance of degrees of freedom estimation in asymmetric GARCH models with t-student innovations." Brazilian Review of Econometrics 40, no. 2 (April 30, 2021): 347–73. http://dx.doi.org/10.12660/bre.v40n22020.80292.

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This work investigates the effects of using the independent Jeffreys prior for the degrees of freedom parameter of a t-student model in the asymmetric generalised autoregressive conditional heteroskedasticity (GARCH) model. To capture asymmetry in the reaction to past shocks, smooth transition models are assumed for the variance. We adopt the fully Bayesian approach for inference, prediction and model selection We discuss problems related to the estimation of degrees of freedom in the Student-t model and propose a solution based on independent Jeffreys priors which correct problems in the likelihood function. A simulated study is presented to investigate how the estimation of model parameters in the t-student GARCH model are affected by small sample sizes, prior distributions and misspecification regarding the sampling distribution. An application to the Dow Jones stock market data illustrates the usefulness of the asymmetric GARCH model with t-student errors.

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Alhamzawi, Rahim, and Intisar Ibrahim Allyas. "Inference with Normal-Jeffreys Prior Distributions in Quantile Regression." IOSR Journal of Mathematics 13, no. 03 (May 2017): 04–09. http://dx.doi.org/10.9790/5728-1303030409.

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Rodríguez, Abel. "On the Jeffreys prior for the multivariate Ewens distribution." Statistics & Probability Letters 83, no. 6 (June 2013): 1539–46. http://dx.doi.org/10.1016/j.spl.2013.02.014.

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Rubio, Francisco Javier, and Brunero Liseo. "On the independence Jeffreys prior for skew-symmetric models." Statistics & Probability Letters 85 (February 2014): 91–97. http://dx.doi.org/10.1016/j.spl.2013.11.012.

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Clarke, Bertrand S., and Andrew R. Barron. "Jeffreys' prior is asymptotically least favorable under entropy risk." Journal of Statistical Planning and Inference 41, no. 1 (August 1994): 37–60. http://dx.doi.org/10.1016/0378-3758(94)90153-8.

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Gelman, Andrew. "Bayes, Jeffreys, Prior Distributions and the Philosophy of Statistics." Statistical Science 24, no. 2 (May 2009): 176–78. http://dx.doi.org/10.1214/09-sts284d.

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Kleibergen, Frank, and Herman K. van Dijk. "On the Shape of the Likelihood/Posterior in Cointegration Models." Econometric Theory 10, no. 3-4 (August 1994): 514–51. http://dx.doi.org/10.1017/s0266466600008653.

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A vector autoregressive (VAR) model is specified with equation system parameters, which directly reflect the possible cointegrating nature of the analyzed time series. By using a flat/diffuse prior, we show that the marginal posteriors of the parameters of interest (multipliers of the cointegrating vectors) may be nonintegrable and favor difference stationary models in an undesired way. To choose between stationary, cointegrated, and difference stationary models in a meaningful way, the Jeffreys prior principle is used. We investigate the sensitivity of the posterior results with respect to the construction of the Jeffreys prior. In this context, we also analyze the effect of fixed and stochastic initial values. The theoretical results are illustrated by using a VAR model for shortand long–term interest rates in the United States.

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Noor, Farzana, Saadia Masood, Yumna Sabar, Syed Bilal Hussain Shah, Touqeer Ahmad, Asrin Abdollahi, and Ahthasham Sajid. "Bayesian Analysis of Cancer Data Using a 4-Component Exponential Mixture Model." Computational and Mathematical Methods in Medicine 2021 (October 12, 2021): 1–11. http://dx.doi.org/10.1155/2021/6289337.

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Cancer is among the major public health problems as well as a burden for Pakistan. About 148,000 new patients are diagnosed with cancer each year, and almost 100,000 patients die due to this fatal disease. Lung, breast, liver, cervical, blood/bone marrow, and oral cancers are the most common cancers in Pakistan. Perhaps smoking, physical inactivity, infections, exposure to toxins, and unhealthy diet are the main factors responsible for the spread of cancer. We preferred a novel four-component mixture model under Bayesian estimation to estimate the average number of incidences and death of both genders in different age groups. For this purpose, we considered 28 different kinds of cancers diagnosed in recent years. Data of registered patients all over Pakistan in the year 2012 were taken from GLOBOCAN. All the patients were divided into 4 age groups and also split based on genders to be applied to the proposed mixture model. Bayesian analysis is performed on the data using a four-component exponential mixture model. Estimators for mixture model parameters are derived under Bayesian procedures using three different priors and two loss functions. Simulation study and graphical representation for the estimates are also presented. It is noted from analysis of real data that the Bayes estimates under LINEX loss assuming Jeffreys’ prior is more efficient for the no. of incidences in male and female. As far as no. of deaths are concerned again, LINEX loss assuming Jeffreys’ prior gives better results for the male population, but for the female population, the best loss function is SELF assuming Jeffreys’ prior.

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Scholl, Holger R. "Shannon optimal priors on independent identically distributed statistical experiments converge weakly to Jeffreys' prior." Test 7, no. 1 (June 1998): 75–94. http://dx.doi.org/10.1007/bf02565103.

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Yosboonruang, Noppadon, Sa-aat Niwitpong, and Suparat Niwitpong. "Measuring the dispersion of rainfall using Bayesian confidence intervals for coefficient of variation of delta-lognormal distribution: a study from Thailand." PeerJ 7 (July 22, 2019): e7344. http://dx.doi.org/10.7717/peerj.7344.

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Since rainfall data series often contain zero values and thus follow a delta-lognormal distribution, the coefficient of variation is often used to illustrate the dispersion of rainfall in a number of areas and so is an important tool in statistical inference for a rainfall data series. Therefore, the aim in this paper is to establish new confidence intervals for a single coefficient of variation for delta-lognormal distributions using Bayesian methods based on the independent Jeffreys’, the Jeffreys’ Rule, and the uniform priors compared with the fiducial generalized confidence interval. The Bayesian methods are constructed with either equitailed confidence intervals or the highest posterior density interval. The performance of the proposed confidence intervals was evaluated using coverage probabilities and expected lengths via Monte Carlo simulations. The results indicate that the Bayesian equitailed confidence interval based on the independent Jeffreys’ prior outperformed the other methods. Rainfall data recorded in national parks in July 2015 and in precipitation stations in August 2018 in Nan province, Thailand are used to illustrate the efficacy of the proposed methods using a real-life dataset.

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Al omari, Mohammed Ahmed. "Bayesian using Importance Sampling Technique of Weibull Regression with Type II Censored Data." European Journal of Mathematics and Statistics 2, no. 3 (June 23, 2021): 10–18. http://dx.doi.org/10.24018/ejmath.2021.2.3.19.

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Keeping in view the Bayesian approach, the study aims to develop methods through the utilization of Jeffreys prior and modified Jeffreys prior to the covariate obtained by using the Importance sampling technique. For maximum likelihood estimator, covariate parameters, and the shape parameter of Weibull regression distribution with the censored data of Type II will be estimated by the study. It is shown that the obtained estimators in closed forms are not available, but through the usage of appropriate numerical methods, they can be solved. The mean square error is the criterion of comparison. With the use of simulation, performances of these three estimates are assessed, bearing in mind different censored percentages, and various sizes of the sample.

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Mohammed Ahmed, Dr Al Omari. "Bayesian Methods and Maximum Likelihood Estimations of Exponential Censored Time Distribution with Cure Fraction." Academic Journal of Applied Mathematical Sciences, no. 72 (March 6, 2021): 106–12. http://dx.doi.org/10.32861/ajams.72.106.112.

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This paper is focused on estimating the parameter of Exponential distribution under right-censored data with cure fraction. The maximum likelihood estimation and Bayesian approach were used. The Bayesian method is implemented using gamma, Jeffreys, and extension of Jeffreys priors with two loss functions, which are; squared error loss function and Linear Exponential Loss Function (LINEX). The methods of the Bayesian approach are compared to maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) to determine the best for estimating the parameter of Exponential distribution under right-censored data with cure fraction. The results show that the Bayesian with gamma prior under LINEX loss function is a better estimation of the parameter of Exponential distribution with cure fraction based on right-censored data.

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Guillotte, Simon, and François Perron. "Bayesian estimation of a bivariate copula using the Jeffreys prior." Bernoulli 18, no. 2 (May 2012): 496–519. http://dx.doi.org/10.3150/10-bej345.

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Gu, Xiaojing, Peng Zhou, and Xingsheng Gu. "Bayesian compressive sensing for thermal imagery using Gaussian-Jeffreys prior." Infrared Physics & Technology 83 (June 2017): 51–61. http://dx.doi.org/10.1016/j.infrared.2017.04.005.

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ISWARI, ANAK AGUNG ISTRI AGUNG CANDRA, I. WAYAN SUMARJAYA, and I. GUSTI AYU MADE SRINADI. "ANALISIS REGRESI BAYES LINEAR SEDERHANA DENGAN PRIOR NONINFORMATIF." E-Jurnal Matematika 3, no. 2 (May 31, 2014): 38. http://dx.doi.org/10.24843/mtk.2014.v03.i02.p064.

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The aim of this study is to apply Bayesian simple linear regression using noninformative prior. The data used in this study is 30 observational data with error generated from normal distribution. The noninformative prior was formed using Jeffreys’ rule. Computation was done using the Gibbs Sampler algorithm with 10.000 iteration. We obtain the following estimates for the parameters, with 95% Bayesian confidence interval (0,775775; 2,626025), with 95% Bayesian confidence interval (2,948; 3,052), and with 95% Bayesian confidence interval (0,375295; 1,114). These values are not very different compared to the actual value of the parameters.

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Yosboonruang, Noppadon, Sa-Aat Niwitpong, and Suparat Niwitpong. "Confidence intervals for rainfall dispersions using the ratio of two coefficients of variation of lognormal distributions with excess zeros." PLOS ONE 17, no. 3 (March 23, 2022): e0265875. http://dx.doi.org/10.1371/journal.pone.0265875.

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Rainfall fluctuation is directly affected by the Earth’s climate change. It can be described using the coefficient of variation (CV). Similarly, the ratio of CVs can be used to compare the rainfall variation between two regions. The ratio of CVs has been widely used in statistical inference in a number of applications. Meanwhile, the confidence interval constructed with this statistic is also of interest. In this paper, confidence intervals for the ratio of two independent CVs of lognormal distributions with excess zeros using the fiducial generalized confidence interval (FGCI), Bayesian methods based on the left-invariant Jeffreys, Jeffreys rule, and uniform priors, and the Wald and Fieller log-likelihood methods are proposed. The results of a simulation study reveal that the highest posterior density (HPD) Bayesian using the Jeffreys rule prior method performed the best in terms of the coverage probability and the average length for almost all cases of small sample size and a large sample size together with a large variance and a small proportion of non-zero values. The performance of the statistic is demonstrated on two rainfall datasets from the central and southern regions in Thailand.

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Song, Chengyuan, Dongchu Sun, Kun Fan, and Rongji Mu. "Posterior Propriety of an Objective Prior in a 4-Level Normal Hierarchical Model." Mathematical Problems in Engineering 2020 (February 14, 2020): 1–10. http://dx.doi.org/10.1155/2020/8236934.

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The use of hierarchical Bayesian models in statistical practice is extensive, yet it is dangerous to implement the Gibbs sampler without checking that the posterior is proper. Formal approaches to objective Bayesian analysis, such as the Jeffreys-rule approach or reference prior approach, are only implementable in simple hierarchical settings. In this paper, we consider a 4-level multivariate normal hierarchical model. We demonstrate the posterior using our recommended prior which is proper in the 4-level normal hierarchical models. A primary advantage of the recommended prior over other proposed objective priors is that it can be used at any level of a hierarchical model.

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Junnumtuam, Sunisa, Sa-Aat Niwitpong, and Suparat Niwitpong. "A Zero-and-One Inflated Cosine Geometric Distribution and Its Application." Mathematics 10, no. 21 (October 28, 2022): 4012. http://dx.doi.org/10.3390/math10214012.

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Count data containing both excess zeros and ones occur in many fields, and the zero-and-one inflated distribution is suitable for analyzing them. Herein, we construct confidence intervals (CIs) for the parameters of the zero-and-one inflated cosine geometric (ZOICG) distribution constructed by using five methods: a Wald CI based on the maximum likelihood estimate, equal-tailed Bayesian CIs based on the uniform or Jeffreys prior, and the highest posterior density intervals based on the uniform or Jeffreys prior. Their efficiencies were compared in terms of their coverage probabilities and average lengths via a simulation study. The results show that the highest posterior density intervals based on the uniform prior performed the best in most cases. The number of new daily COVID-19-related deaths in Luxembourg in 2020 involving data with a high proportion of zeros and ones were analyzed. It was found that the ZOICG model was appropriate for this scenario.

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Khan, Nida, and Muhammad Aslam. "Statistical Analysis of Location Parameter of Inverse Gaussian Distribution Under Noninformative Priors." Journal of Quantitative Methods 3, no. 2 (August 31, 2019): 62–76. http://dx.doi.org/10.29145/2019/jqm/030204.

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Bayesian estimation for location parameter of the inverse Gaussian distribution is presented in this paper. Noninformative priors (Uniform and Jeffreys) are assumed to be the prior distributions for the location parameter as the shape parameter of the distribution is considered to be known. Four loss functions: Squared error, Trigonometric, Squared logarithmic and Linex are used for estimation. Bayes risks are obtained to find the best Bayes estimator through simulation study and real life data

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Rubin, Donald B., and Nathaniel Schenker. "Logit-Based Interval Estimation for Binomial Data Using the Jeffreys Prior." Sociological Methodology 17 (1987): 131. http://dx.doi.org/10.2307/271031.

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Martin, Gael M., and Vance L. Martin. "Bayesian inference in the triangular cointegration model using a jeffreys prior." Communications in Statistics - Theory and Methods 29, no. 8 (January 2000): 1759–85. http://dx.doi.org/10.1080/03610920008832577.

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Fonseca, Thaís C. O., Helio S. Migon, and Marco A. R. Ferreira. "Bayesian analysis based on the Jeffreys prior for the hyperbolic distribution." Brazilian Journal of Probability and Statistics 26, no. 4 (November 2012): 327–43. http://dx.doi.org/10.1214/11-bjps142.

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A, LAVANYA, and LEO ALEXANDER T. "Bayesian estimation of auc of a constant shape bi- weibull failure time distribution." Journal of Management and Science 7, no. 1 (June 30, 2017): 76–91. http://dx.doi.org/10.26524/jms.2017.10.

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A Receiver Operating Characteristic (ROC) curve provides quick access to the quality of classification in many medical diagnoses. The Weibull distribution has been observed as one of the most useful distributions, for modeling and analyzing lifetime data in Engineering, Biology, Survival and other fields. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. In this paper, we examine the performance of Bayesian Estimator using Jeffreys‘ Prior Information and Extension of Jeffreys‘ Prior Information with three Loss functions, namely, the Linear Exponential Loss,General Entropy Loss, and Square Error Loss for estimating the AUC values for Constant Shape Bi-Weibull failure time distribution. Theoretical results are validated by simulation studies. Simulations indicated that estimate of AUC values were good even for relatively small sample sizes (n=25). When AUC≤0.6, which indicated a marked overlap between the outcomes in diseased and non-diseased populations. An illustrative example is also provided to explain the concepts.

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Yosboonruang, Noppadon, Sa-Aat Niwitpong, and Suparat Niwitpong. "Bayesian computation for the common coefficient of variation of delta-lognormal distributions with application to common rainfall dispersion in Thailand." PeerJ 10 (February 4, 2022): e12858. http://dx.doi.org/10.7717/peerj.12858.

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Rainfall fluctuation makes precipitation and flood prediction difficult. The coefficient of variation can be used to measure rainfall dispersion to produce information for predicting future rainfall, thereby mitigating future disasters. Rainfall data usually consist of positive and true zero values that correspond to a delta-lognormal distribution. Therefore, the coefficient of variation of delta-lognormal distribution is appropriate to measure the rainfall dispersion more than lognormal distribution. In particular, the measurement of the dispersion of precipitation from several areas can be determined by measuring the common coefficient of variation in the rainfall from those areas together. Herein, we compose confidence intervals for the common coefficient of variation of delta-lognormal distributions by employing the fiducial generalized confidence interval, equal-tailed Bayesian credible intervals incorporating the independent Jeffreys or uniform priors, and the method of variance estimates recovery. A combination of the coverage probabilities and expected lengths of the proposed methods obtained via a Monte Carlo simulation study were used to compare their performances. The results show that the equal-tailed Bayesian based on the independent Jeffreys prior was suitable. In addition, it can be used the equal-tailed Bayesian based on the uniform prior as an alternative. The efficacies of the proposed confidence intervals are demonstrated via applying them to analyze daily rainfall datasets from Nan, Thailand.

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Tomazella, Vera Lucia Damasceno, Sandra Rêgo Jesus, Amanda Buosi Gazon, Francisco Louzada, Saralees Nadarajah, Diego Carvalho Nascimento, Francisco Aparecido Rodrigues, and Pedro Luiz Ramos. "Bayesian Reference Analysis for the Generalized Normal Linear Regression Model." Symmetry 13, no. 5 (May 12, 2021): 856. http://dx.doi.org/10.3390/sym13050856.

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This article proposes the use of the Bayesian reference analysis to estimate the parameters of the generalized normal linear regression model. It is shown that the reference prior led to a proper posterior distribution, while the Jeffreys prior returned an improper one. The inferential purposes were obtained via Markov Chain Monte Carlo (MCMC). Furthermore, diagnostic techniques based on the Kullback–Leibler divergence were used. The proposed method was illustrated using artificial data and real data on the height and diameter of Eucalyptus clones from Brazil.

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Doster, W. "Jeffreys’ prior is the Hausdorff measure for the Hellinger and Kullback-Leibler distances." Studia Scientiarum Mathematicarum Hungarica 36, no. 1-2 (June 1, 2000): 25–34. http://dx.doi.org/10.1556/sscmath.36.2000.1-2.4.

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Fouskakis, Dimitris, and Ioannis Ntzoufras. "Information consistency of the Jeffreys power-expected-posterior prior in Gaussian linear models." METRON 75, no. 3 (May 23, 2017): 371–80. http://dx.doi.org/10.1007/s40300-017-0110-6.

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Assoudou, Souad, and Belkheir Essebbar. "A Bayesian model for binary Markov chains." International Journal of Mathematics and Mathematical Sciences 2004, no. 8 (2004): 421–29. http://dx.doi.org/10.1155/s0161171204202319.

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This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC) techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.

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Wu, Min, Fode Zhang, Yimin Shi, and Yan Wang. "Statistical Analysis for Competing Risks’ Model with Two Dependent Failure Modes from Marshall–Olkin Bivariate Gompertz Distribution." Computational Intelligence and Neuroscience 2022 (May 28, 2022): 1–18. http://dx.doi.org/10.1155/2022/3988225.

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The bivariate or multivariate distribution can be used to account for the dependence structure between different failure modes. This paper considers two dependent competing failure modes from Gompertz distribution, and the dependence structure of these two failure modes is handled by the Marshall–Olkin bivariate distribution. We obtain the maximum likelihood estimates (MLEs) based on classical likelihood theory and the associated bootstrap confidence intervals (CIs). The posterior density function based on the conjugate prior and noninformative (Jeffreys and Reference) priors are studied; we obtain the Bayesian estimates in explicit forms and construct the associated highest posterior density (HPD) CIs. The performance of the proposed methods is assessed by numerical illustration.

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Ahmadini, Abdullah Ali H., Amara Javed, Sohail Akhtar, Christophe Chesneau, Farrukh Jamal, Shokrya S. Alshqaq, Mohammed Elgarhy, Sanaa Al-Marzouki, M. H. Tahir, and Waleed Almutiry. "Robust Assessing the Lifetime Performance of Products with Inverse Gaussian Distribution in Bayesian and Classical Setup." Mathematical Problems in Engineering 2021 (October 4, 2021): 1–9. http://dx.doi.org/10.1155/2021/4582958.

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The inverse Gaussian (Wald) distribution belongs to the two-parameter family of continuous distributions having a range from 0 to ∞ and is considered as a potential candidate to model diffusion processes and lifetime datasets. Bayesian analysis is a modern inferential technique in which we estimate the parameters of the posterior distribution obtained by formally combining a prior distribution with an observed data distribution. In this article, we have attempted to perform the Bayesian and classical analyses of the Wald distribution and compare the results. Jeffreys' and uniform priors are used as noninformative priors, while the exponential distribution is used as an informative prior. The analysis comprises finding joint posterior distributions, the posterior means, predictive distributions, and credible intervals. To illustrate the entire estimation procedure, we have used real and simulated datasets, and the results thus obtained are discussed and compared. We have used the Bayesian specialized Open BUGS software to perform Markov Chain Monte Carlo (MCMC) simulations using a real dataset.

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Yanuar, Ferra, Hazmira Yozza, and Ratna Vrima Rescha. "Comparison of Two Priors in Bayesian Estimation for Parameter of Weibull Distribution." Science and Technology Indonesia 4, no. 3 (July 31, 2019): 82. http://dx.doi.org/10.26554/sti.2019.4.3.82-87.

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This present study purposes to conduct Bayesian inference for scale parameters, denoted by , from Weibull distribution. The prior distribution chosen in this study is the prior conjugate, that is inverse gamma and non-informative prior, namely Jeffreys’ prior. This research also aims to study several theoretical properties of posterior distribution based on prior used and then implement it to generated data and make comparison between both Bayes estimator as well. The method used to evaluate the best estimator is based on the smallest Mean Square Error (MSE). This study proved that Bayes estimator using conjugate prior produces parameter value that is better estimate than the non-informative prior since it produces smaller MSE value, for condition scale parameter value more than one based on analytic and simulation study. Meanwhile for scale parameter value less than one, it could not yielded the good estimated value.

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Mattingly, Henry H., Mark K. Transtrum, Michael C. Abbott, and Benjamin B. Machta. "Maximizing the information learned from finite data selects a simple model." Proceedings of the National Academy of Sciences 115, no. 8 (February 6, 2018): 1760–65. http://dx.doi.org/10.1073/pnas.1715306115.

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We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by the available data, we find that this prior puts weight only on boundaries of the parameter space. Thus, it selects a lower-dimensional effective theory in a principled way, ignoring irrelevant parameter directions. In the limit where there are sufficient data to tightly constrain any number of parameters, this reduces to the Jeffreys prior. However, we argue that this limit is pathological when applied to the hyperribbon parameter manifolds generic in science, because it leads to dramatic dependence on effects invisible to experiment.

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Collins‐Elliott, S. A. "Quantifying artefacts over time: Interval estimation of a Poisson distribution using the Jeffreys prior." Archaeometry 61, no. 5 (July 28, 2019): 1207–22. http://dx.doi.org/10.1111/arcm.12481.

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Yang, Jianfei, Dirk H. J. Poot, Matthan W. A. Caan, Tanja Su, Charles B. L. M. Majoie, Lucas J. van Vliet, and Frans M. Vos. "Reliable Dual Tensor Model Estimation in Single and Crossing Fibers Based on Jeffreys Prior." PLOS ONE 11, no. 10 (October 19, 2016): e0164336. http://dx.doi.org/10.1371/journal.pone.0164336.

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M. Al-Athari, Faris, and Khaled K. Jaber. "Bayesian estimation for the symmetric double Pareto distribution with multi-parameter Jeffreys prior information." International Journal of Academic Research 5, no. 3 (May 20, 2013): 36–45. http://dx.doi.org/10.7813/2075-4124.2013/5-3/a.6.

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Cheema, Ammara Nawaz, Muhammad Aslam, Ibrahim M. Almanjahie, and Ishfaq Ahmad. "Bayesian Modeling of 3-Component Mixture of Exponentiated Inverted Weibull Distribution under Noninformative Prior." Mathematical Problems in Engineering 2020 (July 29, 2020): 1–11. http://dx.doi.org/10.1155/2020/8765321.

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Bayesian study of 3-component mixture modeling of exponentiated inverted Weibull distribution under right type I censoring technique is conducted in this research work. The posterior distribution of the parameters is obtained assuming the noninformative (Jeffreys and uniform) priors. The different loss functions (squared error, quadratic, precautionary, and DeGroot loss function) are used to obtain the Bayes estimators and posterior risks. The performance of the Bayes estimators through posterior risks under the said loss functions is investigated through simulation process. Real data analysis of tensile strength of carbon fiber is also applied for 3 components to conclude the presentation of Bayes estimators. The limiting expressions are also elaborated for Bayes estimators and posterior risks in this study. The impact of some test termination times and sample sizes is reported on Bayes estimators.

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Saputro, D. R. S., F. Amalia, P. Widyaningsih, and R. C. Affan. "Parameter estimation of multivariate multiple regression model using bayesian with non-informative Jeffreys’ prior distribution." Journal of Physics: Conference Series 1022 (May 2018): 012002. http://dx.doi.org/10.1088/1742-6596/1022/1/012002.

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Chao, J. C., and P. C. B. Phillips. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior." Journal of Econometrics 87, no. 1 (November 1998): 49–86. http://dx.doi.org/10.1016/s0304-4076(98)00006-2.

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Journal articles on the topic 'Jeffreys prior'

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