This study focuses on estimating the reliability of a multicomponent stress-strength model using two Bayesian approaches‎: ‎E-Bayesian and hierarchical Bayesian‎. ‎This model follows Inverse Rayleigh distributions with distinct parameters‎. ‎Additionally‎, ‎the efficiency of the proposed methods is compared by employing Monte Carlo simulation and analyzing a data set.

When spatial data are realizations of a Gaussian model with parametric mean and covariance functions, then the function of observations that minimizes mean square prediction error depends on some unknown parameters. Usually, these parameters are replaced by their estimates to obtain the plug-in predictor. But, this method has some problems in estimation of the parameters and the optimality and mean square error of the spatial predictor. In this paper, the problems related to plug-in method are discussed and to avoid them, the Bayesian approach for spatial prediction is proposed. Then the Bayesian spatial prediction for Gaussian and trans Gaussian models according to observations, that may contain noise, are derived. Next, in a simulation study, the adequacy of Bayesian prediction is compared with plug-in prediction. Finally, a numerical example illustrates the Bayesian spatial prediction of rainfall in a region at the north of Iran.

‎The recent advancements in technology have faced an increase in the growth rate of data‎.‎According to the amount of data generated‎, ‎ensuring effective analysis using traditional approaches becomes very complicated‎.‎One of the methods of managing and analyzing big data is classification‎.‎%One of the data mining methods used commonly and effectively to classify big data is the MapReduce‎‎In this paper‎, ‎the feature weighting technique to improve Bayesian classification algorithms for big data is developed based on Correlative Naive Bayes classifier and MapReduce Model‎.‎%Classification models include Naive Bayes classifier‎, ‎correlated Naive Bayes and correlated Naive Bayes with feature weighting‎.‎Correlated Naive Bayes classification is a generalization of the Naive Bayes classification model by considering the dependence between features‎.‎%This paper uses the feature weighting technique and Laplace calibration to improve the correlated Naive Bayes classification‎.‎The performance of all described methods are evaluated by considering accuracy‎, ‎sensitivity and specificity‎, ‎accuracy‎, ‎sensitivity and specificity metrics.

This article examines statistical inference for R= P(Y<X) where X and Y are independent but not identically distributed Pareto of the first kind (Pareto (I)) random variables with same scale parameter but different shape parameters. The Maximum likelihood, uniformly minimum variance unbiased and Bayes estimators with Gamma prior are used for this purpose. Simulation studies which compare the estimators are presented. Moreover, sensitivity of Bayes estimator to the prior parameters is considered.