Interval-censored data consist of adjacent inspection times that surround an unknown failure time. We have in this paper reviewed the classical approach which is maximum likelihood in estimating the Weibull parameters with interval-censored data. We have also considered the Bayesian approach in estimating the Weibull parameters with interval-censored data under three loss functions. This study ...

We consider the chain ladder reserving method in a Bayesian set up, which allows for combining individual claims development data with portfolio information as for instance development patterns from industry-wide data. We derive the Bayes estimators and the credibility estimators within this Bayesian framework. We show that the credibility estimators are exact Bayesian in the case of the expone...

In this paper, we investigate a Bayesian sparse reconstruction algorithm called compressive sensing via Bayesian support detection (CS-BSD). This algorithm is quite robust against measurement noise and achieves the performance of an minimum mean square error (MMSE) estimator that has support knowledge beyond a certain SNR thredhold. The key idea behind CS-BSD is that reconstruction takes a dete...

This paper is concerned with the estimation of the number of species in a population through a fully hierarchical Bayesian models using the Metropoliswithin-Gibbs algorithm. The proposed Bayesian estimator is based on Poisson random variables with means that are distributed according to some prior distributions with unknown hyperparameters. An empirical Bayes approach is considered and compared...

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a set of multiple parameters, which can be divided into two disjoint subsets. On one set, a frequentist method may be favored and on the other, the Bayesian. ...

There are two major routes to address linear inverse problems. Whereas regularization-based approaches build estimators as solutions of penalized regression optimization problems, Bayesian estimators rely on the posterior distribution of the unknown, given some assumed family of priors. While these may seem radically different approaches, recent results have shown that, in the context of additi...

Various Bayesian wavelet estimators have been proposed recently in literature. Following Bayesian approach, a prior distribution is imposed on wavelet coefficients of the unknown response function and a Bayesian estimator is obtained then by applying a suitable Bayesian rule to the resulting posterior distribution of the coefficients. Numerous simulations studies demonstrate the good performanc...

While the classical framework has a rich set of limited information procedures such as GMM and other related methods, the situation is not so in the Bayesian framework. We develop a limited information procedure in the Bayesian framework that does not require the knowledge of the full likelihood. The developed procedure is a Bayesian counterpart of the classical GMM but has advantages over the ...

Estimation theory has been developed over centuries. There are several approaches to utilizing this theory; in this chapter, these approaches are classified into three types. Type I includes the oldest two methods, the least squares (LS) and moment methods; both of these methods are non-optimal estimators. The least squares method was introduced by Carl Friedrich Gauss. Least squares problems f...

in this paper, a bayesian approach is proposed for shift point detection in an inverse gaussian distribution. in this study, the mean parameter of inverse gaussian distribution is assumed to be constant and shift points in shape parameter is considered. first the posterior distribution of shape parameter is obtained. then the bayes estimators are derived under a class of priors and using variou...