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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]

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]

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]

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]