This paper presents a Bayesian nonparametric approach to the estimation of a system and its components’ survival functions arising from observing the failure of a series system or a competing-risks model. A Dirichlet multivariate process is used as a prior for the vector of the components’ random subsurvival function to derive the Bayes estimator of the survival function when the cause of failu...

Whereas classical data processing techniques work with perfect models, or models with dynamical white noise, geophysical sciences have to deal with imperfect models containing spatially structured errors. For the perfect model cases, in terms of Mean-Field Markovian processes, the optimal filter is known: the Kalman estimator is the answer to the linear Gaussian problem and in the general case ...

In the estimation of a multivariate normal mean, it is shown that the problem of deriving shrinkage estimators improving on the maximum likelihood estimator can be reduced to that of solving an integral inequality. The integral inequality not only provides a more general condition than a conventional differential inequality studied in the literature, but also handles non-differentiable or disco...

In certain auction, search, and related models, the boundary of the support of the observed data depends on some of the parameters of interest. For such nonregular models, standard asymptotic distribution theory does not apply. Previous work has focused on characterizing the nonstandard limiting distributions of particular estimators in these models. In contrast, we study the problem of constru...

The empirical Bayes estimator is applied to software failures production. The time between failures data registered up to a given time, are used in order to estimate the probability of failure appearance during the next interval time. This method is similar to the estimation of n-grams in natural language processing. A modified expression to the estimator usually used in language and speech pro...

Abstract-This paper presents the reliability computation and Bayesian estimation of system reliability when the applied stress and strength follows the power function distribution. The Power Function Distribution is considered as a simple model to assess component reliability and may exhibit a better fit for failure data and also provide more appropriate information about hazard rate. The resul...

To estimate a success probability p, two experiments are available: individual Bernoulli(p) trials or the product of r individual Bernoulli(p) trials. This problem has its roots in reliability where either single components can be tested or a system of r identical components can be tested. A total of N experiments can be performed, and the problem is to sequentially select some combination (all...

Bayesian phylogenetic methods are generating noticeable enthusiasm in the field of molecular systematics. Many phylogenetic models are often at stake and different approaches are used to compare them within a Bayesian framework. The Bayes factor, defined as the ratio of the marginal likelihoods of two competing models, plays a key role in Bayesian model selection. We focus on an alternative est...

Parameter estimation for the K distribution is an essential part of the statistical analysis of non-Rayleigh sonar reverberation or clutter for performance prediction, estimation of scattering properties, and for use in signal and information processing algorithms. Computational issues associated with maximum likelihood (ML) estimation techniques for K-distribution parameters often force the us...