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Tweedie exponential dispersion (TED) process is a large class of generalized stochastic process, which includes the commonly used Wiener process, Gamma process and inverse Gausssian process as special cases. In this paper, we propose an accelerated degradation model based on the TED process, and then apply the objective Bayesian method to make inferences on the model. The Jeffreys prior and reference priors under different group orderings are derived, and the posterior property based on each prior is then validated. A simulation study is carried out to assess the performance of the proposed Bayesian method in comparison with the maximum-likelihood estimation (MLE), and finally the method is applied to analyse a real degradation dataset. [ABSTRACT FROM AUTHOR]

Abstract.Many procedures can assess the equivalence of the means or medians between groups when comparing several independent populations. However, neither the mean nor median captures the entire distribution. We propose a Bayesian approach for the quantiles of several normal distributions, focusing on developing non informative priors to compare the quantiles of multiple populations. Further, reference priors and first- and second-order matching priors are developed. The second-order matching prior does not exist, and the reference priors do not satisfy a first-order matching criterion. In addition, conditions for proper posterior distributions for general priors, including developed priors, are provided. Finally, simulations include a real-world example to demonstrate the proposed approach. The numerical studies indicate that the matching prior performs better than the reference prior and Jeffreys’ prior in terms of matching the frequentist target coverage probabilities, and shows good performance even in small sample sizes. Moreover, the matching prior is not affected by the values of parameters, the number of populations, and does not depend on the values of pth quantile [ABSTRACT FROM AUTHOR]

Bayesian Hierarchical models has been widely used in modern statistical application. To deal with the data having complex structures, we propose a generalized hierarchical normal linear (GHNL) model which accommodates arbitrarily many levels, usual design matrices and ‘vanilla’ covariance matrices. Objective hyperpriors can be employed for the GHNL model to express ignorance or match frequentist properties, yet the common objective Bayesian approaches are infeasible or fraught with danger in hierarchical modelling. To tackle this issue, [Berger, J., Sun, D., & Song, C. (2020b). An objective prior for hyperparameters in normal hierarchical models. Journal of Multivariate Analysis, 178, 104606. https://doi.org/10.1016/j.jmva.2020.104606] proposed a particular objective prior and investigated its properties comprehensively. Posterior propriety is important for the choice of priors to guarantee the convergence of MCMC samplers. James Berger conjectured that the resulting posterior is proper for a hierarchical normal model with arbitrarily many levels, a rigorous proof of which was not given, however. In this paper, we complete this story and provide an user-friendly guidance. One main contribution of this paper is to propose a new technique for deriving an elaborate upper bound on the integrated likelihood, but also one unified approach to checking the posterior propriety for linear models. An efficient Gibbs sampling method is also introduced and outperforms other sampling approaches considerably.

In this paper, a competing risks model with dependent causes of failure is considered under left-truncated and right-censoring scenario. When the dependent failure causes follow a Marshall–Olkin bivariate exponential distribution, estimation of model parameters and reliability indices are proposed from classic and Bayesian approaches, respectively. Maximum likelihood estimators and approximate confidence intervals are constructed, and conventional Bayesian point and interval estimations are discussed as well. In addition, E-Bayesian estimators are proposed and their asymptotic behaviors have been investigated. Further, another objective-Bayesian analysis is also proposed when a noninformative probability matching prior is used. Finally, extensive simulation studies are carried out to investigate the performance of different methods. Two real data examples are presented to illustrate the applicability. [ABSTRACT FROM AUTHOR]

In Bayesian quantile smoothing spline [Thompson, P., Cai, Y., Moyeed, R., Reeve, D., & Stander, J. (2010). Bayesian nonparametric quantile regression using splines. Computational Statistics and Data Analysis, 54, 1138–1150.], a fixed-scale parameter in the asymmetric Laplace likelihood tends to result in misleading fitted curves. To solve this problem, we propose a new Bayesian quantile smoothing spline (NBQSS), which considers a random scale parameter. To begin with, we justify its objective prior options by establishing one sufficient and one necessary condition of the posterior propriety under two classes of general priors including the invariant prior for the scale component. We then develop partially collapsed Gibbs sampling to facilitate the computation. Out of a practical concern, we extend the theoretical results to NBQSS with unobserved knots. Finally, simulation studies and two real data analyses reveal three main findings. Firstly, NBQSS usually outperforms other competing curve fitting methods. Secondly, NBQSS considering unobserved knots behaves better than the NBQSS without unobserved knots in terms of estimation accuracy and precision. Thirdly, NBQSS is robust to possible outliers and could provide accurate estimation.

This paper provides an objective Bayesian inference method with partial information based on generalized Type-II progressive hybrid censored data. We first derive a reference prior with partial information on the unknown parameters and then show that this leads to suitable posterior distributions. In addition, we provide a prediction method based on the derived reference prior with partial information for the remaining service life when a unit has survived until a certain time point. The validity of the proposed approach is assessed through Monte Carlo simulations and a real data analysis. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Shanghai University of Engineering Science / Shanghai Gongcheng Jishu Daxue Xuebao is the property of Journal of Shanghai University of Engineering Science Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Shanghai University of Engineering Science / Shanghai Gongcheng Jishu Daxue Xuebao is the property of Journal of Shanghai University of Engineering Science Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The Wiener process as a degradation model plays an important role in the degradation analysis. In this paper, we propose an objective Bayesian analysis for an acceleration degradation Wiener model which is subjected to measurement errors. The Jeffreys prior and reference priors under different group orderings are first derived, the propriety of the posteriors is then validated. It is shown that two of the reference priors can yield proper posteriors while the others cannot. A simulation study is carried out to investigate the frequentist performance of the approach compared to the maximum likelihood method. Finally, the approach is applied to analyse a real data.

Summary: Bayes factors that do not require prior distributions are proposed for testing one parametric model versus another. These Bayes factors are relatively simple to compute, relying only on maximum likelihood estimates, and are Bayes consistent at an exponential rate for nested models even when the smaller model is true. These desirable properties derive from the use of data splitting. Large sample properties, including consistency, of the Bayes factors are derived, and a simulation study explores practical concerns. The methodology is illustrated with civil engineering data involving compressive strength of concrete. [ABSTRACT FROM AUTHOR]

In this paper we address estimation and prediction problems for extreme value distributions under the assumption that the only available data are the record values. We provide some properties and pivotal quantities, and derive unbiased estimators for the location and rate parameters based on these properties and pivotal quantities. In addition, we discuss mean-squared errors of the proposed estimators and exact confidence intervals for the rate parameter. In Bayesian inference, we develop objective Bayesian analysis by deriving non informative priors such as the Jeffrey, reference, and probability matching priors for the location and rate parameters. We examine the validity of the proposed methods through Monte Carlo simulations for various record values of size and present a real data set for illustration purposes. [ABSTRACT FROM AUTHOR]

In this paper, we provide an entropy inference method that is based on an objective Bayesian approach for upper record values having a two-parameter logistic distribution. We derive the entropy that is based on the i-th upper record value and the joint entropy that is based on the upper record values. Moreover, we examine their properties. For objective Bayesian analysis, we obtain objective priors, namely, the Jeffreys and reference priors, for the unknown parameters of the logistic distribution. The priors are based on upper record values. Then, we develop an entropy inference method that is based on these objective priors. In real data analysis, we assess the quality of the proposed models under the objective priors and compare them with the model under the informative prior. [ABSTRACT FROM AUTHOR]

In this study, we address inference problems for Gumbel distribution when the available data are lower record values. We first derive unbiased estimators of unknown parameters, and then, we construct an exact confidence interval for the scale parameter and a predictive interval for the next lower value by deriving certain properties and pivotal quantities. These are compared with the results for existing inference. For Bayesian inference, we derive noninformative priors such as the Jeffreys and reference priors for unknown parameters and examine whether they satisfy the probability matching criteria; then, we apply them to develop objective Bayesian analysis. [ABSTRACT FROM AUTHOR]

Abstract: The goal of the present paper is to report on some recent advances, which we have made over the last five years, in spatial interpolation and sampling design in case of uncertainty about the parameters of common geostatistical models and non-Gaussianity of observations. In particular, we consider copula-based approaches to spatial interpolation when the observations are distinctly non-Gaussian and then report on criteria and methods for choosing default priors for Bayesian spatial interpolation and for choosing optimal designs based on (transformed) Gaussian kriging. For most of the interpolation and design methods presented in this paper we provide free source code in MATLAB/Octave language. [Copyright &y& Elsevier]

Problems involving thousands of null hypotheses have been addressed by estimating the local false discovery rate (LFDR). A previous LFDR approach to reporting point and interval estimates of an effect-size parameter uses an estimate of the prior distribution of the parameter conditional on the alternative hypothesis. That estimated prior is often unreliable, and yet strongly influences the posterior intervals and point estimates, causing the posterior intervals to differ from fixedparameter confidence intervals, even for arbitrarily small estimates of the LFDR. That influence of the estimated prior manifests the failure of the conditional posterior intervals, given the truth of the alternative hypothesis, to match the confidence intervals. Those problems are overcome by changing the posterior distribution conditional on the alternative hypothesis from a Bayesian posterior to a confidence posterior. Unlike the Bayesian posterior, the confidence posterior equates the posterior probability that the parameter lies in a fixed interval with the coverage rate of the coinciding confidence interval. The resulting confidence- Bayes hybrid posterior supplies interval and point estimates that shrink toward the null hypothesis value. The confidence intervals tend to be much shorter than their fixed-parameter counterparts, as illustrated with gene expression data. Simulations nonetheless confirm that the shrunken confidence intervals cover the parameter more frequently than stated. Generally applicable sufficient conditions for correct coverage are given. In addition to having those frequentist properties, the hybrid posterior can also be motivated from an objective Bayesian perspective by requiring coherence with some default prior conditional on the alternative hypothesis. That requirement generates a new class of approximate posteriors that supplement Bayes factors modified for improper priors and that dampen the influence of proper priors on the credibility intervals. While that class of posteriors intersects the class of confidence- Bayes posteriors, neither class is a subset of the other. In short, two first principles generate both classes of posteriors: a coherence principle and a relevance principle. The coherence principle requires that all effect size estimates comply with the same probability distribution. The relevance principle means effect size estimates given the truth of an alternative hypothesis cannot depend on whether that truth was known prior to observing the data or whether it was learned from the data. [ABSTRACT FROM AUTHOR]

Fundamentals of the Research: When the progressing process is taken to be account, it's seen that the approaches on statistics have polarized between two pivots. Despite of the domination of Classical approach in statistics, Bayesian approach has also crucial arguments. It's needed to clarify the descriptions of both aspects about statistical concepts by compiling them. Besides, using "prior information", that is main difference from Classical one, created the discussion of objective and subjective Bayesian analysis. Thus, compilation of concepts and launching a current discussion are the main motivations that lead to this study. Purpose of the Research: The purpose of the study is to express the distinctions between Bayesian approach and Classical approach on the basis of statistical concepts. Data Sources: No data is used at the study due to not to be intended to do an application. Main Discussion: In the context of this stated purpose, at first, the dissimilarities that become clear in the description of uncertainty and probability are tried to be described. Again by regarding the distinctions of the approaches, Parameter, Point Estimation, Confidence Interval and Hypothesis Testing that are the main subjects of statistical inference are touched on. Since using the prior information, Bayesian approach produces different results from Classical one, so it has been criticized, claiming as to be subjective. Actually Bayesian approach also has been discussing the objectivity and subjectivity since it's seen variety on the application Bayesian method. In the study, merely as an introduction, this discussion relating the Bayesian schools is considered. Results: From both aspects, the distinctions of the concepts that have key role in statistical inference are emphasized. It's enlightened the discussion of objective - subjective Bayesian Analysis by means of introducing the current views in the literature. [ABSTRACT FROM AUTHOR]

Abstract: Gaussian Markov random fields (GMRF) are important families of distributions for the modeling of spatial data and have been extensively used in different areas of spatial statistics such as disease mapping, image analysis and remote sensing. GMRFs have been used for the modeling of spatial data, both as models for the sampling distribution of the observed data and as models for the prior of latent processes/random effects; we consider mainly the former use of GMRFs. We study a large class of GMRF models that includes several models previously proposed in the literature. An objective Bayesian analysis is presented for the parameters of the above class of GMRFs, where explicit expressions for the Jeffreys (two versions) and reference priors are derived, and for each of these priors results on posterior propriety of the model parameters are established. We describe a simple MCMC algorithm for sampling from the posterior distribution of the model parameters, and study frequentist properties of the Bayesian inferences resulting from the use of these automatic priors. Finally, we illustrate the use of the proposed GMRF model and reference prior for studying the spatial variability of lip cancer cases in the districts of Scotland over the period 1975–1980. [Copyright &y& Elsevier]

This article reviews power priors, a class of prior distributions for an unknown parameter that exploits information from results of previous, similar studies, a situation arising often in clinical trials. The article shows that, for independent and identically distributed historical data, a basic formulation of power priors (geometric priors) can be obtained as the result of a prior updating-and-combining process based on training samples of iid historical data. This formulation gives an operational justification to power priors. It also allows us to relate the discount scalar quantity controlling the influence of historical information on final inference to the size of training samples. Properties of power priors and their extension to more complex set-ups are discussed. Then several examples are provided of their use in the analysis of clinical trials data. The approach is shown to be appropriate for handling problems arising when information is combined from different studies, such as lack of exchangeability between preceding and current data, and the risk that prior information overwhelms evidence from the study in question. [ABSTRACT FROM AUTHOR]

This article considers a robust Bayesian approach to the sample size determination problem. We focus on global Bayesian robustness that studies lower bound (Ln), upper bound (Un), and range (Rn) of posterior quantities of interest, obtained as the prior varies in a class of distributions. Specifically, we are interested in the selection of an appropriate sample size that gives guarantees to the researcher of observing a small value of the range and, depending on the problems, either a sufficiently large lower bound or a sufficiently small upper bound. Toward this end, we approach the problem as a design issue and provide new sample size determination criteria based on summaries of the predictive distributions of Ln, Un, and Rn, such as expectations and tail probabilities. Relationships and comparison to standard classical and (nonrobust) Bayesian methods are discussed. The proposed methods are studied for the normal model with conjugate priors and used for choosing the size of a clinical trial. [ABSTRACT FROM AUTHOR]

The interest in the study of record statistics has been increasing in recent years in the context of predicting stock markets and addressing global warming and climate change problems such as cyclones and floods. However, because record values are mostly rare observed, its probability distribution may be skewed or asymmetric. In this case, the Bayesian approach with a reasonable choice of the prior distribution can be a good alternative. This paper presents an objective Bayesian method for predicting future record values when observed record values have a two-parameter exponentiated Gumbel distribution with the scale and shape parameters. For objective Bayesian analysis, objective priors such as the Jeffreys and reference priors are first derived from the Fisher information matrix for the scale and shape parameters, and an analysis of the resulting posterior distribution is then performed to examine its properness and validity. In addition, under the derived objective prior distributions, a simple algorithm using a pivotal quantity is proposed to predict future record values. To validate the proposed approach, it was applied to a real dataset. For a closer examination and demonstration of the superiority of the proposed predictive method, it was compared to time-series models such as the autoregressive integrated moving average and dynamic linear model in an analysis of real data that can be observed from an infinite time series comprising independent sample values. [ABSTRACT FROM AUTHOR]