The method of determining Bayesian estimators for the special ratios of variance components called the intraclass correlation coefficients is presented. The exact posterior distribution for these ratios of variance components is obtained. The approximate posterior mean of this distribution is also derived. All computations are non-iterative and avoid numerical integration.
We carry out Bayesian inference for the Jelinski-Moranda and Littlewood software failure models given a sample of failure times. Furthermore, we illustrate how to assess the optimal length of an additional pre-release testing period under each of these models. Modern Bayesian computational methods are used to estimate the posterior expected utility of testing for and additional time.
This paper deals with the problem of prediction of the order statistics in a future sample. Underlying model is exponential. Outlier is present in the sample drawn and the sample size is considered a random variable. Firstly, an outlier of type θδ in the exponential model, is treated. Actual predictive distribution of the order statistics is obtained. As an extension, the two-sample problem is also taken up. Finally, an outlier of type θ + δ is dealt with and now the predictive distribution is expressed...
We consider the joint modelling of the mean and covariance structures for the general antedependence model, estimating their parameters and the innovation variances in a longitudinal data context. We propose a new and computationally efficient classic estimation method based on the Fisher scoring algorithm to obtain the maximum likelihood estimates of the parameters. In addition, we also propose a new and innovative Bayesian methodology based on the Gibbs sampling, properly adapted for longitudinal...
The purpose of this paper is to study Bayesian like R- and M-estimators of change point(s). These estimators have smaller variance than the related argmax type estimators. Confidence intervals for the change point based on the exchangeability arguments are constructed. Finally, theoretical results are illustrated on the real data set.
The paper concerns estimation of the rose of directions of a stationary fibre process in from the intersection counts of the process with test planes. A new approach is suggested based on Bayesian statistical techniques. The method is derived from the special case of a Poisson line process however the estimator is shown to be consistent generally. Markov chain Monte Carlo (MCMC) algorithms are used for the approximation of the posterior distribution. Uniform ergodicity of the algorithms used is...
Hydrology and water resources management are inherently affected by uncertainty in many of their involved processes, including inflows, rainfall, water demand, evaporation, etc. Statistics plays, therefore, an essential role in their study. We review here some recent advances within Bayesian statistics and decision analysis which will have a profound impact in these fields.
This text describes a method of estimating the hazard rate of survival data following monotone Aalen regression model. The proposed approach is based on techniques which were introduced by Arjas and Gasbarra [4]. The unknown functional parameters are assumed to be a priori piecewise constant on intervals of varying count and size. The estimates are obtained with the aid of the Gibbs sampler and its variants. The performance of the method is explored by simulations. The results indicate that the...
This paper considers Bayesian parameter estimation and an associated adaptive control scheme for controlled Markov chains and diffusions with time-averaged cost. Asymptotic behaviour of the posterior law of the parameter given the observed trajectory is analyzed. This analysis suggests a "cost-biased" estimation scheme and associated self-tuning adaptive control. This is shown to be asymptotically optimal in the almost sure sense.
2000 Mathematics Subject Classification: 62E16, 65C05, 65C20.We consider the problem of predictive interval for future observations from Weibull distribution. We consider two cases they are: (i) fixed sample size (FSS), (ii) random sample size (RSS). Further, we derive the predictive function for both FSS and RSS in closed forms. Next, the upper and lower 1%, 2.5%, 5% and 10% critical points for the predictive functions are calculated. To show the usefulness of our results, we present some simulation...
This article deals with the objective Bayesian analysis of random censorship model with informative censoring using Weibull distribution. The objective Bayesian analysis has a long history from Bayes and Laplace through Jeffreys and is reaching the level of sophistication gradually. The reference prior method of Bernardo is a nice attempt in this direction. The reference prior method is based on the Kullback-Leibler divergence between the prior and the corresponding posterior distribution and easy...
This paper discusses the Bayesian reliability analysis for an exponential failure mode on the basis of some ordered observations when the first p observations may represent early failures or outliers. The Bayes estimators of the mean life and reliability are obtained for the underlying parametric model referred to as the SB(p) model under the assumption of the squared error loss function, the inverted gamma prior for scale parameter and a generalized uniform prior for the nuisance parameter.
In this paper, the Bayesian analysis of the survival data arising from a Rayleigh model is carried out under the assumption that the clinical study based on n patients is terminated at the dth death, for some preassigned d (0 < d ≤ n), resulting in the survival times t1 ≤ t2 ≤ ... ≤ td, and (n - d) survivors. For the prior knowledge about the Rayleigh parameter, the gamma density, the inverted gamma density, and the beta density of the second kind are respectively assumed, and for each of...
In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...
In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...