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The problem of sample size estimation is important in medical applications, especially in cases of expensive measurements
of immune biomarkers. This paper describes the problem of logistic regression analysis with the sample
size determination algorithms, namely the methods of univariate statistics, logistics regression, cross-validation and
Bayesian inference. The authors, treating the regression model parameters as multivariate variable, propose to estimate
the sample size using the distance between parameter distribution functions on cross-validated data sets.
Herewith, the authors give a new contribution to data mining and statistical learning, supported by applied mathematics.

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‎There are different types of classification methods for classifying the certain data‎. ‎All the time the value of the variables is not certain and they may belong to the interval that is called uncertain data‎. ‎In recent years‎, ‎by assuming the distribution of the uncertain data is normal‎, ‎there are several estimation for the mean and variance of this distribution‎. ‎In this paper‎, ‎we consider the mean and variance for each of the start and end of intervals‎. ‎Thus we assume that the distribution of uncertain data is bivariate normal distribution‎. ‎We used the maximum likelihood to estimate the means and variances of the bivariate normal distribution‎. ‎Finally‎, ‎Based on the Naive Bayesian classification‎, ‎we propose a Bayesian mixture algorithm for classifying the certain and uncertain data‎. ‎The experimental results show that the proposed algorithm has high accuracy.

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‎A Bayesian network is a graphical model that represents a set of random variables and their causal relationship via a Directed Acyclic Graph (DAG)‎. ‎There are basically two methods used for learning Bayesian network‎: ‎parameter-learning and structure-learning‎. ‎One of the most effective structure-learning methods is K2 algorithm‎. ‎Because the performance of the K2 algorithm depends on node ordering‎, ‎more effective node ordering inference methods are needed‎. ‎In this paper‎, ‎based on the fact that the parent and child variables are identified by estimated Markov Blanket (MB)‎, ‎we first estimate the MB of a variable using Grow-Shrink algorithm‎, ‎then determine the candidate parents of a variable by evaluating the conditional frequencies using Dirichlet probability density function‎. ‎Then the candidate parents are used as input for the K2 algorithm‎. ‎Experimental results for most of the datasets indicate that our proposed method significantly outperforms previous method‎.  

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‎Dynamic panel data models include the important part of medicine‎, ‎social and economic studies‎. ‎Existence of the lagged dependent variable as an explanatory variable is a sensible trait of these models‎. ‎The estimation problem of these models arises from the correlation between the lagged depended variable and the current disturbance‎. ‎Recently‎, ‎quantile regression to analyze dynamic panel data has been taken in to consideration‎. ‎In this paper‎, ‎quantile regression model by adding an adaptive Lasso penalty term to the random effects for dynamic panel data is introduced by assuming correlation between the random effects and initial observations‎. ‎Also‎, ‎this model is illustrated by assuming that the random effects and initial values are independent‎. ‎These two models are analyzed from a Bayesian point of view‎. ‎Since‎, ‎in these models posterior distributions of the parameters are not in explicit form‎, ‎the full conditional posterior distributions of the parameters are calculated and the Gibbs sampling algorithm is used to deduction‎. ‎To compare the performance of the proposed method with the conventional methods‎, ‎a simulation study was conducted and at the end‎, ‎applications to a real data set are illustrated‎.

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‎In this study‎, ‎E-Bayesian of parameters of two parameter exponential distribution under squared error loss function is obtained‎. ‎The estimated and the efficiency of the proposed method has been compared with Bayesian estimator using Monte Carlo simulation‎. 

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‎Analysis of large geostatistical data sets‎, ‎usually‎, ‎entail the expensive matrix computations‎. ‎This problem creates challenges in implementing statistical inferences of traditional Bayesian models‎. ‎In addition,researchers often face with multiple spatial data sets with complex spatial dependence structures that their analysis is difficult‎. ‎This is a problem for MCMC sampling algorithms that are commonly used in Bayesian analysis of spatial models‎, ‎causing serious problems such as slowing down and chain integration‎. ‎To escape from such computational problems‎, ‎we use low-rank models‎, ‎to analyze Gaussian geostatistical data‎. ‎This models improve MCMC sampler convergence rate and decrease sampler run-time by reducing parameter space‎. ‎The idea here is to assume‎, ‎quite reasonably‎, ‎that the spatial information available from the entire set of observed locations can be summarized in terms of a smaller‎, ‎but representative‎, ‎sets of locations‎, ‎or ‘knots’‎. ‎That is‎, ‎we still use all of the data but we represent the spatial structure through a dimension reduction‎. ‎So‎, ‎again‎, ‎in implementing the reduction‎, ‎we need to design the knots‎. ‎Consideration of this issue forms the balance of the article‎. ‎To evaluate the performance of this class of models‎, ‎we conduct a simulation study as well as analysis of a real data set regarding the quality of underground mineral water of a large area in Golestan province‎, ‎Iran‎.

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‎WinBUGS is one of the usual softwares in computational Bayesian statistics‎, ‎which is used to fit Baysian models easily‎. ‎Although this software has usual mathematical functions and statistical distributions as built in functions‎, ‎sometimes it is necessary to include other functions and distributions in computations which is done by some tricks and indirectly‎. ‎By using WinBUGS development interface (known as WBDev)‎, ‎new mathematical functions and statistical distributions can be added in the software‎. ‎This method facilitates writing codes of statistical models‎, ‎increases speed of computations and make computations more efficient‎. ‎In this paper‎, ‎the stages of including new mathematical functions and statistical distributions in the WinBUGS are illustrated by some examples‎.

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‎In this study‎, ‎E-Bayesian and hierarchical Bayesian of parameter of Rayleigh distribution under progressive type-II censoring sampales and the efficiency of the proposed methods has been compared with each and Bayesian estimator using Monte Carlo simulation‎.

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In this paper, ‎reliability in multi-component stress-strength models‎, ‎when the stress and strength variables are inverse Rayleigh distributions with different parameters of alpha and beta. ‎Estimates of the maximum likelihood‎, ‎Bayesian and empirical Bayesian are estimated‎. ‎Then‎, ‎with the help of Monte Carlo simulation and two real data sets‎, ‎these estimation methods are compared‎.

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‎Tree models represent a new and innovative way of analyzing large data sets by dividing predictor space into simpler areas‎. ‎Bayesian Additive Regression Trees model‎, ‎a model that we explain in this article‎, ‎uses a totality of trees in its structure‎, ‎since the combination of several trees from a tree only has a higher accuracy‎.

‎Then‎, ‎this model is a tree-based model and a nonparametric model that uses general aggregation methods‎, ‎and boosting algorithms in particular and in fact is extension of the classification and Regression Tree methods in which the decision tree exists in the structure of these methods‎.

‎In this method‎, ‎on the parameters of the model sum of tree and put regular prior then use the boosting algorithms for analysis‎. ‎In this paper‎, ‎first the Bayesian Additive Regression Trees model is introduced and then applied in survival analysis of lung cancer patients‎.

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In the analysis of Bernoulli's variables, an investigation of the their dependence is of the prime importance. In this paper, the distribution of the Markov logarithmic series is introduced by the execution of the first-order dependence among Bernoulli variables. In order to estimate the parameters of this distribution, maximum likelihood, moment, Bayesian and also a new method which called the expected Bayesian method (E-Bayesian) are employed. In continuation, using a simulation study, it is shown that the expected Bayesian estimator out performed over the other estimators.

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Whenever approximate and initial information about the unknown parameter of a distribution is available, the shrinkage estimation method can be used to estimate it. In this paper, first, the E-Bayesian estimation of the parameter of an inverse Rayleigh distribution under the general entropy loss function is obtained. Then, the shrinkage estimate of the inverse Rayleigh distribution parameter is investigated using the guess value. Also, using Monte Carlo simulations and a real data set, the proposed shrinkage estimation is compared with the UMVU and E-Bayesian estimators based on the relative efficiency criterion.

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The Internet of Things is suggested as the upcoming revolution in the Information and communication technology due to its very high capability of making various businesses and industries more productive and efficient. This productivity comes from the emergence of innovation and the introduction of new capabilities for businesses. Different industries have shown varying reactions to IOT, but what is clear is that IOT has applications in all Businesses. These applications have made significant progress in some industries such as health and transportation but is under development in others, namely agriculture and animal husbandry. In fact, the production of data bases on the Internet of Things is one of the main pillars in the field of big data and data science, Therefore, statistical concepts and models that are used in data science can be beneficially implemented in such data. Among the valid statistical models, Bayesian statistics for data is being utilized in these studies. In this research the fundamentals of Bayesian statistics for big data and most notably the data produced by IOT is explained. They have been Pragmatically examined in both road traffic as well as people’s social behavior towards using vehicles, which have had practically and scientifically valid results.
 

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Thomas Bayes, the founder of Bayesian vision, entered the University of
Edinburgh in 1719 to study logic and theology. Returning in 1722, he worked with
his father in a small church. He also was a mathematician and in 1740 he made a
novel discovery which he never published, but his friend Richard Price found it in his
notes after his death in 1761, reedited
it and published it. But until Laplace, no one
cared until the late 18th century, when data did not have equal confidence in Europe.
Pierre − Simon Laplace, a young mathematician, believed that probability theory was
a key in his hand, and he independently discovered the Bayesian mechanism and published
it in 1774. Laplace expressed the principle not in an equation but in words.
Today, Bayesian statistics as a discipline of statistical philosophy and the interpretation of probability is very important and has become known as the Bayesian theorem
presented after Bayesian death. Allen Turing is a British computer scientist, mathematician
and philosopher who is now known as the father of computer science and artificial
intelligence. His outstanding achievements during his short life are the result of the
adventures of a beautiful mind that was finally extinguished forever with a suspicious
death. During World War II, Turing worked in Belchley Park, the center of the British
decipherment, and for a time was in charge of the German Navy’s cryptographic analysis.
He devised several methods, specifically from Bayesian’s point of view, without
breaking his name to crack German codes, as well as the electromechanical machine
method that could find the features of the Enigma machine. Finding Enigma can also
be considered one of his great works. Alan Turing was a leading scientist who played
an important role in the development of computer science and artificial intelligence and
the revival of Bayesian thought. Turing provided an effective and stimulating contribution
to artificial intelligence through the Turing experiment. He then worked at the
National Physics Laboratory in the United Kingdom, presenting one of the prototypes
of a stored computer program, though it worked, which was not actually made as the
”Manchester Mark ”. He went to the University of Manchester in 1948 to be recognized
as the world’s first real computer. However, later on, the role of Bayesian rule and law
in scientific developments becomes more important. Many possible Bayesian methods
in the 21st century have made significant advances in the explanation and application of
Bayesian statistics in climate development and have solved many of the world’s problems.
New global technology has grown on Bayesian ideas, which will be reviewed intion of probability is very important and has become known as the Bayesian theorem
presented after Bayesian death. Allen Turing is a British computer scientist, mathematician
and philosopher who is now known as the father of computer science and artificial
intelligence. His outstanding achievements during his short life are the result of the
adventures of a beautiful mind that was finally extinguished forever with a suspicious
death. During World War II, Turing worked in Belchley Park, the center of the British
decipherment, and for a time was in charge of the German Navy’s cryptographic analysis.
He devised several methods, specifically from Bayesian’s point of view, without
breaking his name to crack German codes, as well as the electromechanical machine
method that could find the features of the Enigma machine. Finding Enigma can also
be considered one of his great works. Alan Turing was a leading scientist who played
an important role in the development of computer science and artificial intelligence and
the revival of Bayesian thought. Turing provided an effective and stimulating contribution
to artificial intelligence through the Turing experiment. He then worked at the
National Physics Laboratory in the United Kingdom, presenting one of the prototypes
of a stored computer program, though it worked, which was not actually made as the
”Manchester Mark ”. He went to the University of Manchester in 1948 to be recognized
as the world’s first real computer. However, later on, the role of Bayesian rule and law
in scientific developments becomes more important. Many possible Bayesian methods
in the 21st century have made significant advances in the explanation and application of
Bayesian statistics in climate development and have solved many of the world’s problems.
New global technology has grown on Bayesian ideas, which will be reviewed in this article.

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Today, the diagnosis of diseases using artificial intelligence and machine learning algorithms are of great importance, because by using the data available in the study field of the desired disease, useful information and results can be obtained that reduce the occurrence of many deaths. Among these diseases, we can mention the diagnosis of diabetes, which has spread today due to the growth of urban life and the decrease in people's activity. So, it is very important to know whether a person is suffering from diabetes or not. In this article, the data set related to the information of people who have done the diabetes diagnosis test is used, this information is related to 520 people. People are classified into two groups based on whether their diabetes test result is positive or not, and Bayesian classification methods such as Bayesian Support Vector Machine, Naive Bayes, CNK and CatBoost ensemble classification method have been used to conclude which of these The methods can have a better ability to analyze the data and also to compare these methods use accuracy, precision, F1-score, recall, ROC diagram.

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In ‎this ‎article, ‎queunig ‎model ‎‎$‎M/M/1‎$ ‎is ‎Considered, ‎in ‎which ‎the ‎innterarrival ‎of ‎customers ‎have ‎an ‎exponenial ‎disributon ‎with ‎the ‎parameter ‎‎$‎lambda‎$ ‎and ‎the ‎service ‎times‎ ‎have ‎an ‎exponenial ‎disributon with the ‎parameter ‎‎$‎mu‎$ ‎and ‎are ‎independent ‎of ‎the ‎interarrival ‎times.‎ ‎it ‎is ‎also ‎assumed ‎that ‎the ‎system ‎is ‎active ‎until ‎‎$‎T‎$‎. Then, under this stopping time Bayesian, ‎$‎E‎$‎-Bayesian and hierarchical Bayesian estima‎‏‎tion‎s of the traffic intensity parameter of this queuing model are obtained under the general entropy loss function and considering the gamma and erlang prior distributions for parameters ‎$‎lambda‎$ ‎and ‎‎$‎mu‎$‎, respicctively. Then, using numerical analysis and based on a new index, Bayesian, ‎$‎E‎$‎-Bayesian and hierarchical Bayesian estima‎‏‎tion‎s are compared.

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The statistical inference of the multi-component stress-strength parameter, $R_{s,k}$, is considered in the three-parameter Weibull distribution. The problem is studied in two cases. In the first case, assuming that the stress and strength variables have common shape and location parameters and non-common scale parameters and all these parameters are unknown, the maximum likelihood estimation and the Bayesian estimation of the parameter $‎R_{s,k}$ are investigated. In this case, as the Bayesian estimation does not have a closed form, it is approximated by two methods, Lindley and $mbox{MCMC}$. Also, asymptotic confidence intervals have been obtained. In the second case, assuming that the stress and strength variables have known common shape and location parameters and non-common and unknown scale parameters, the maximum likelihood estimation, the uniformly minimum variance unbiased estimators, the exact Bayesian estimation of the parameter $‎R_{s,k}$ and the asymptotic confidence interval is calculated. Finally, using Monte Carlo simulation, the performance of different estimators has been compared.

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Marshall-Olkin introduced a family of distributions which obtained by adding a parameter into other distributions. Santoz-Neto etal study an extended Weibull distribution. In this paper two Raiyle and Pareto extended weibull are studied under some momemts and Bayesian methods with some loss functions such as squared error, entropy, linex, squared error in logarithm and modified linex. Also the MCMC method are study for these two distributions.

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    We live in the information age, constantly surrounded by vast amounts of data from the world around us. To utilize this information effectively, it must be mathematically expressed and analyzed using statistics.
     Statistics play a crucial role in various fields, including text mining, which has recently garnered significant attention. Text mining is a research method used to identify patterns in texts, which can be in written, spoken, or visual forms.
      The applications of text mining are diverse, including text classification, clustering, web mining, sentiment analysis, and more. Text mining techniques are utilized to assign numerical values to textual data, enabling statistical analysis.
       Since working with data requires a solid foundation in statistics, statistical tools are employed in text analysis to make predictions, such as forecasting changes in stock prices or currency exchange rates based on current textual data. 
       By leveraging statistical methods, text mining can uncover, confirm, or refute the truths hidden within textual content. Today, this topic is widely used in machine learning. This paper aims to provide a basic understanding of statistical tools in text mining and demonstrates how these powerful tools can be used to analyze and interpret events.