‎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.

In the estimation of a probability density function (PDF) by kernel method, two inherent problems are the choice of sampling methods and the selection of a bandwidth. In this article, we use the balanced and unbalanced ranked set sampling (RSS) methods and Bayesian bandwidth to estimate a PDF by kernel method. To compare our method with existing methods, we use an extensive simulation study to compare the RSS with simple random sampling (SRS) PDF estimator and also Bayesian bandwidth with other existing bandwidths. As an application, we use the household expenses and income data of the Statistical Center of Iran in 2021 to estimate the PDF of the total expenses of the households in Tehran province.

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as com-pared to simple models. This paper considers mixture of Topp-Leone distributions under classical and Bayesian perspective based on com-plete sample. The new distribution which exhibits decreasing and up-side down bathtub shaped density while the distribution has the ability to model lifetime data with decreasing, increasing and upside down bathtub shaped failure rates. We derive several properties of the new distribution such as moments, moment generating function, conditional moment, mean deviation, Bonferroni and Lorenz curves and the order statistics of the proposed distribution. Moreover, we estimate the pa-rameters of the model by using frequentist and Bayesian approaches. For Bayesian analysis, , ve loss functions, namely the squared error loss function (SELF), weighted squared error loss function (WSELF), mod-i, ed squared error loss function (MSELF), precautionary loss function (PLF), and K-loss function (KLF) and uniform as well as gamma pri-ors are considered to obtain the Bayes estimators and posterior risk of the unknown parameters of the model. Furthermore, credible intervals (CIs) and highest posterior density (HPD) intervals are also obtained. Monte Carlo simulation study is done to access the behavior of these estimators. For the illustrative purposes, a real-life application of the proposed distribution to a tensile strength data set is provided.

In statistics‎, ‎errors are inherent in data and models‎, ‎particularly heteroscedasticity and skew-normal error structures‎. ‎These errors were simultaneously generated and infused into the data‎, ‎leading to uncertainty in parameter estimation‎. ‎The statistician uses statistical knowledge to elicit information and guide decision-making‎. ‎Both classical and Bayesian restricted Stein-rule least squares were compared when the data were contaminated with the aforementioned errors‎. ‎This study proposed an innovative Bayesian generalized restricted Stein-rule least squares method with heteroscedastic skew-normal errors‎, ‎which was ultimately found to be more efficient compared to non-Bayesian restricted Stein-rule least square estimators‎. ‎The study observed excellent performance of the Bayesian frameworks‎, ‎including the Bayes estimate and posterior mean‎, ‎in comparison to the classical restricted Stein-rule least squares estimators‎. ‎Therefore‎, ‎the study recommends Bayesian generalized restricted Stein-rule least squares to analysts and researchers who may encounter such errors in their data‎.

The Exponentiated Gumbel (EG) distribution has been proposed to capture some aspects of the data that the Gumbel distribution fails to specify. In this paper, we estimate the EG’s parameters in the Bayesian framework. We consider a 2-level hierarchical structure for prior distribution.As the posterior distributions do not admit a closed form, we do an approximated inference by using Gibbs and Metropolis-Hastings algorithm.

Precise identification of the time when a process has changed enables process engineers to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for a Poisson process in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change, a linear trend and a known multiple number of changes in the Poisson rate. The Markov chain Monte Carlo is used to obtain posterior distributions of the change point parameters and corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the well-known c-, Poisson exponentially weighted moving average (EWMA) and Poisson cumulative sum (CUSUM) control charts for different change type scenarios. We also apply the Deviance Information Criterion as a model selection criterion in the Bayesian context, to find the best change point model for a given dataset where there is no prior knowledge about the change type in the process. In comparison with built-in estimators of EWMA and CUSUM charts and ML based estimators, the Bayesian estimator performs reasonably well and remains a strong alternative. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

In this study, based on Bayesian Generalized Linear Models, correlation between the parameters of two Poisson distributions was computed. Due to lack of the closed form for posterior distribution, hierarchical Bayesian statistics using the Metropolis- Hastings algorithm to calculate the correlation of two Poisson distributions is presented. In this regard, the highest posterior density for coefficient of variation in the model are calculated. Using Bayesian Deviance Information Criterion (DIC) has been shown that a Poisson- lognormal model can assess the correlation between the parameters better than the Poisson-gamma model. Finally, the proposed method is used to simulated data of BANK TEJARAT.