The Bayesian Variable Selection analysis is widely used as a new methodology in air quality control trials and generalized linear models. One of the important and, of course, controversial topics in this area is Selection of prior distribution of unknown model parameters. The aim of this study is presenting a substitution for mixture of priors which besides preservation of benefits and computational efficiencies obviate the available paradoxes and contradictions. In this research we pay attention to two points of view,empirical and fully Bayesian. Especially, a mixture of priors and its theoretical characteristics is introduced. Finally, the proposed model is illustrated with a real example.

Background: A pre-surgical evaluation of cognitive functions in patients with mesial temporal lobe epilepsy (mTLE) is critical. The limitations of the usual brain analysis model were resolved by the spatial Bayesian Variable Selection (SBVS) method. An Ising and Dirichlet Process (Ising-DP) model considers SBVS and the grouping of a large number of voxels. The present study aimed to identify brain areas involved in episodic memory in patients with right mTLE and controls via the Ising-DP model. The model was extended to include between-subject factors (BSFs), and the results were compared with other classical methods. Methods: The present cross-sectional study was conducted on 15 patients with right mTLE and 20 controls in Tehran, Iran, in 2018. During functional magnetic resonance imaging, the subjects were tested with the face-encoding memory task, followed by a recognition memory test. The participants demographic factors such as age, sex, marital status, area of residence, and years of schooling were considered to comprise BSFs. The independent t test, the chi-square test, and the correlation test were conducted using the SPSS software (version 20. 0). The image processing was carried out using SPM (version 12. 0) and MATLAB (version R2014a). Results: The Ising-DP model appropriately (R2=0. 642) detected activated hippocampal areas. The model adjusted for BSFs indicated a better fit by the significant effect of age (P[γ ]>0. 91), sex (P[γ ]>0. 87), and years of schooling (P[γ ]>0. 89). The heat maps exhibited decreased activation in the right hippocampal region in the patients compared with the controls (P<0. 0001). Right hippocampal activity had a significant positive correlation with the recognition memory test in the mTLE group (r=0. 665) and the control group (r=0. 593). Conclusion: The Ising-DP model was sufficiently sensitive to detect activated areas in our patients with right mTLE during the face-encoding memory task. Since the model adjusted for BSFs improved sensitivity, we recommend the use of more detailed BSFs such as seizure history in future research.

Risk identification, impact assessment, and response planning constitute three building blocks of project risk management. Correspondingly, three types of interactions could be envisioned between risks, between impacts of several risks on a portfolio component, and between several responses. While the interdependency of risks is a well-recognized issue, the other two types of interactions remain unacknowledged in the risk response planning literature. This research suggests a Bayesian belief network for modeling portfolio risks, their impacts, and responses. There are three kinds of nodes in this network: nodes representing portfolio risks, nodes corresponding to risk impacts on each objective of each portfolio component, and nodes showing response actions. The problem is to decide which responses are to be selected. For this purpose, an optimization model is proposed that minimizes the sum of both residual risk effects on portfolio component objectives and response implementation costs. Subsequently, a genetic algorithm is introduced to solve the model. A simple portfolio instance is also provided to illustrate the proposed model.