In the meta-analysis of clinical trials, usually the data of each trail summarized by one or more outcome measure estimates which reported along with their standard errors. In the case that summary data are multi-dimensional, usually, the data analysis will be performed in the form of a number of separated univariate analysis. In such a case the correlation between summary statistics would be ignored. In contrast, a multivariate meta-analysis model, use from these correlations synthesizes the outcomes, jointly to estimate the multiple pooled effects simultaneously. In this paper, we present a Nonparametric Bayesian bivariate random effect meta-analysis.

‎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.

Nonlinear regression models have widespread applications across diverse scientific disciplines‎. ‎Achieving precise fitting of the optimal nonlinear model is essential‎, ‎taking into account the biases inherent in Bayesian optimal design‎. ‎This study introduces a Bayesian optimal design utilizing the Dirichlet process as a prior‎. ‎The Dirichlet process is a fundamental tool in exploring Nonparametric Bayesian inference‎, ‎providing multiple well-suited representations‎. ‎The research paper presents a novel one-parameter model‎, ‎termed the ``unit-exponential distribution"‎, ‎specifically designed for the unit interval‎. ‎Additionally‎, ‎a representation is employed to approximate the D-optimality criterion‎, ‎considering the Dirichlet process as a functional tool‎. ‎Through this approach‎, ‎the aim is to identify a Nonparametric Bayesian optimal design.

Introduction: Parkinson disease is a neurodegenerative disease that disrupts functional brain networks. Many neurodegenerative disorders are associated with changes in brain communication patterns. Resting-state functional connectivity studies can distinguish the topological structure of Parkinson patients from healthy individuals by analyzing patterns between different regions of the brain. Accordingly, the present study aimed to determine the brain topological features and functional connectivity in patients with Parkinson disease, using a Bayesian approach. Methods: The data of this study were downloaded from the open neuro site. These data include resting-state functional magnetic resonance imaging (rs-fMRI) of 11 healthy individuals and 11 Parkinson patients with mean ages of 64. 36 and 63. 73, respectively. An advanced Nonparametric Bayesian model was used to evaluate topological characteristics, including clustering of brain regions and correlation coefficient of the clusters. The significance of functional relationships based on each edge between the two groups was examined through false discovery rate (FDR) and network-based statistics (NBS) methods. Results: Brain connectivity results showed a major difference in terms of the number of regions in each cluster and the correlation coefficient between the patient and healthy groups. The largest clusters in the patient and control groups were 26 and 53 regions, respectively, with clustering correlation values of 0. 36 and 0. 26. Although there are 15 common areas across the two clusters, the intensity of the functional relationship between these areas was different in the two groups. Moreover, using NBS and FDR methods, no significant difference was observed for each edge between the patient and healthy groups (P>0. 05). Conclusion: The results of this study show a different topological configuration of the brain network between the patient and healthy groups, indicating changes in the functional relationship between a set of areas of the brain.

In this paper‎, ‎we study a Nonparametric Bayesian inference on the family of nonincreasing density functions on real positive data‎. ‎One interesting problem is the goodness of fit test in such a context‎. ‎In other words‎, ‎we consider Nonparametric Bayesian testing on the family of nonincreasing density in this domain‎. ‎So‎, ‎we define Nonparametric hypothesis testing and compare two different testing approaches‎. ‎The first approach is given based on the Bayes factor‎. ‎This approach is the well-known Bayesian approach for testing‎, ‎although its computation is complicated‎. ‎Decision-theoretic considerations with the loss function drive the second approach for a given distance‎. ‎This second approach has the advantage of considering the distance to the null hypothesis but needs the definition of a threshold‎. ‎When no threshold is known as a priori‎, ‎a possibility exists to calculate a p-value‎, ‎and the method becomes more complicated to compute‎. ‎We propose a hybrid algorithm to accelerate the computation of the p-value‎. ‎The comparison of both approaches is performed based on a simulation study.