In this study, we study the empirical Bayes estimation of the parameter of the exponential distribution. In the empirical Bayes procedure, we employ the non-parameter polynomial density estimator to the estimation of the unknown marginal probability density function, instead of estimating the unknown prior probability density function of the parameter. Empirical Bayes estimators are derived for...

In this study, the application of Bayes networks and fault tree analysis in reliability estimation have been investigated. Fault tree analysis is one of the most widely used methods for estimating reliability. In recent years, a method called "Bayes Network" has been used, which is a dynamic method, and information about the probable failure of the system components will be updated according to...

In many areas of epidemiologic, demographic and geographical research, inference based on hierarchical spatial regression models is popular and important; for example, in disease mapping, environmental and health monitoring studies. Several estimation and inferential procedures have been proposed for these models, utilizing a variety of methods such as estimating equations, empirical Bayes and ...

‎Consider an estimation problem in a one-parameter non-regular distribution when both endpoints of the support depend on a single parameter‎. ‎In this paper‎, ‎we give sufficient conditions for a generalized Bayes estimator of a parametric function to be admissible‎. ‎Some examples are given‎. ‎

Let X ∼ Np(θ, σIp) and W ∼ σχm, where both θ and σ are unknown, and X is independent of W . Optimal estimation of θ with unknown σ is a fundamental issue in applications but basic theoretical issues remain open. We consider estimation of θ under squared error loss. We develop sufficient conditions for prior density functions such that the corresponding generalized Bayes estimators for θ are adm...

A naive Bayes classifier is a simple probabilistic classifier based on applying Bayes’ theorem with naive independence assumption. The explanatory variables (Xi) are assumed to be independent from the target variable (Y ). Despite this strong assumption this classifier has proved to be very effective on many real applications and is often used on data stream for supervised classification. The n...

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound on the minimax risk, but also characterizes the fundamental limit of any estimator given the prior knowledge. Our bounds are based on the notion of f -inform...

BACKGROUND Exploratory preclinical, as well as clinical trials, may involve a small number of patients, making it difficult to calculate and analyze the pharmacokinetic (PK) parameters, especially if the PK parameters show very high inter-individual variability (IIV). In this study, the performance of a classical first-order conditional estimation with interaction (FOCE-I) and expectation maxim...