Invariant HPD credible sets and MAP estimators
نویسندگان
چکیده
Abstract. MAP estimators and HPD credible sets are often criticized in the literature because of paradoxical behaviour due to a lack of invariance under reparametrization. In this paper, we propose a new version of MAP estimators and HPD credible sets that avoid this undesirable feature. Moreover, in the special case of non-informative prior, the new MAP estimators coincide with the invariant frequentist ML estimators. We also propose several adaptations in the case of nuisance parameters.
منابع مشابه
Bayesian Estimation of Rayleigh Distribution Based on Generalized Order Statistics
Exact expressions for single and product moments of generalized order statistics are derived when the underlying population is assumed to have a Rayleigh distribution. Bayesian estimators and highest posterior density (HPD) credible intervals are obtained for the scale parameter and reliability function based on generalized order statistics. We also derive the Bayes predictive estimator and HPD...
متن کاملBayesian prediction of future observations from inverse Weibull distribution based on type-II hybrid censored sample
In this paper, we have discussed the Bayesian procedure for the prediction of the future samples from inverse Weibull (IW) distribution under Type-II hybrid censoring scheme. Bayes estimators along with the corresponding highest posterior density (HPD) credible intervals have also been constructed for the parameters of IW distribution. The performance of the Bayes estimators of the model parame...
متن کاملEstimation and Hypothesis Testing for Exponential Lifetime Models with Double Censoring and Prior Information
In this paper, on the basis of a doubly censored sample and in a Bayesian framework, the problem of estimating the mean lifetime, hazard rate, and survival function of the exponential lifetime model is addressed. Bayes estimators under squared-error loss functions are obtained in closed forms. Highest posterior density (HPD) estimators and credible intervals are computed using iterative methods...
متن کاملBayesian Analysis of Randomly Censored Generalized Exponential Distribution
Abstract: This paper deals with Bayesian analysis of two-parameter generalized exponential distribution in proportional hazards model of random censorship. It is well known for two-parameter lifetime distributions that continuous conjugate priors for the parameters do not exist; we assume independent gamma priors for the scale and shape parameter. It is seen that the closed-form expressions for...
متن کاملOn the behavior of Bayesian credible intervals for some restricted parameter space problems
For estimating a positive normal mean, Zhang and Woodroofe (2003) as well as Roe and Woodroofe (2000) investigate 100(1 − α)% HPD credible sets associated with priors obtained as the truncation of noninformative priors onto the restricted parameter space. Namely, they establish the attractive lower bound of 1−α 1+α for the frequentist coverage probability of these procedures. In this work, we e...
متن کامل