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.

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.

Importance measures are well-known and important tools which are widely used in risk-informed decision making. Their outstanding traditional definitions have made them useful in many applications related to risk and reliability aspects of different systems. These perfect traditional definitions help researchers to find the most important components in a system, and consequently, to detect and obviate weaknesses in system structure and operations. Generally, these measures are based on fault tree technique. Although fault tree is a powerful tool to study risk, reliability, and structural characteristics of systems, Bayesian networks have indicated explicit advantages over it in modeling and analysis abilities. Classical fault tree is not suitable in analysis of large systems that include aspects such as: common cause failure, redundant failure, uncertainty, and some kind of complex dependencies such as sequentially dependent failures, while these aspects are not negligible in large modern systems anymore. So, the perfect definitions of importance measures are restricted to limitations of fault tree. Bayesian networks, on the other hand, have become a widely used method in different kinds of statistical problems, including fault diagnosis, reliability and safety assessment, and updating safety systems failure probabilities. In addition, Bayesian networks due to their modeling and analytical abilities, are capable of accommodating the mentioned aspects easily and straightforwardly. In this paper, we extend the traditional definitions of importance measures to Bayesian networks resulting in more capable importance measures in terms of modeling and analysis. The importance measures that are extended to Bayesian networks in this research are the most important and widely used ones that some of them are used in famous methods named probabilistic safety assessment. The extended importance measures are: Risk achievement worth, Risk reduction worth, Fussell-Vesely importance measure, Birnbaum importance measure, and Differential importance measure. The results of implementing the new achievements on a real-world case study prove the desired effectiveness.

In some instances, the occurrence of an event can be influenced by its spatial location, giving rise to spatial survival data. The accurate and precise estimation of parameters in a spatial survival model poses a challenge due to the complexity of the likelihood function, highlighting the significance of employing a Bayesian approach in survival analysis. In a Bayesian spatial survival model, the spatial correlation between event times is elucidated using a geostatistical model. This article presents a simulation study to estimate the parameters of classical and spatial survival models, evaluating the performance of each model in fitting simulated survival data. Ultimately, it is demonstrated that the spatial survival model exhibits superior efficacy in analyzing blood cancer data compared to conventional models.

Regression analysis is done, traditionally, considering homogeneity and normality assumption for the response variable distribution. Whereas in many applications, observations indicate to a heterogeneous structure containing some sub-populations with skew-symmetric structure either due to heterogeneity, multimodality or skewness of the population or a combination of them. In this situations, one can use a mixture of skew-symmetric distributions to model the population. In this paper we considered the Bayesian approach of regression analysis under the assumption of heterogeneity of population and a skew-symmetric distribution for sub-populations, by using a mixture of skew normal distributions. We used a simulation study and a real world example to assess the proposed Bayesian methodology and to compare it with frequentist approach.

Modeling correlated ordinal response data is usually more complex than the case of continuous and binary responses. Existing literature lacks an appropriate approach to modeling such data. For small sample sizes, however) these models lose their appeal since their inferences arc based OIl large samples. In this work, the Bayesian analysis of an asymmetric bivariate ordinal latent variable model has been developed. The latent response variable has been chosen to follow the generalized bivariate Gumble distribution. Using some specific priors and MCMC algorithms the regression parameters were estimated. As an application, a data set concerning Diabetic Retinopathy in 116 patients have been analyzed. This data set includes the disease status of each eye for patients as an ordinal response and a number of explanatory variables some of which are common to both eyes and the rest are organ specific.

This paper considers the Bayesian model averaging of inverse Gaussian regression models for regression analysis in situations that the response observations are positive and right-skewed. The computational challenges related to computing the essential quantities for executing of this methodology and their dominating ways are discussed. Providing closed form expressions for the interested posterior quantities and considering suitable prior distributions are two attractive aspects of the proposed methodology. The proposed approach has been evaluated via a simulation study, and its applicability is expressed by using a real example related to the seismic studies.