The copula Gaussian graphical model (CGGM) is one of the major mathematical models for high dimensional biological networks which provides a graphical representation, especially, for sparse networks. Basically, this model uses a regression of the Gaussian graphical model (GGM) whose precision matrix describes the conditional dependence between the variables to estimate the coefficients of the linear regression model. The Bayesian inference for the model parameters is used to overcome the dimensional limitation of GGM under sparse networks and small sample sizes. But from the application in bench-mark data sets, it is seen that although CGGM is successful in certain systems, it may not fit well for non-normal multivariate observations. In this study, we propose the vine copulas to relax the strict normality assumption of CGGM and to describe networks from a variety of copulas’ alternates besides the Gaussian copula. Accordingly, we evaluate the best fitted bivariate copula distribution for every pairwise gene and compute the estimated adjacency matrix which denotes the presence of an edge between the corresponding genes. We assess the performance of our proposed approach in three network data via distinct accuracy measures by comparing the outputs with the results of the CGGM.

One of the sophisticated mathematical techniques for evaluating the relative efficiency of decision-making units (DMUs) in a multi-inputs-output setting is data envelopment analysis. A non-parametric productivity index called the Malmquist index (MI) tracks changes in a DMU’s overall factor output over time. This study seeks to present a broad overview of the changes in the MI for nearly all of the world’s nations over 19 years beginning in 3061. This research evaluates a time series data set made up of 16 economic indexes. Each nation’s MI, which compares 2000 and 2019, shows how each nation has changed over that period. One of the most important purposes of this study comparing the countries by their MI is that it allows for a fair comparison of productivity across different time periods and regions. It also provides insights into the sources of productivity growth, such as changes in technology or improvements in efficiency. As a result, the countries can allocate resources more wisely and develop more effective investment plans by understanding the elements that lead to productivity increase. By implementing some statistical techniques, nations are further divided into four categories based on their MI. Furthermore, a yearly distribution of the MI has been included to illustrate its trends between the years 2000 to 2019. Finally, the changing flow for some countries of each category is shown in three-year tracks.

This paper addresses a critical gap in circular economy (CE) research by introducing a novel methodological framework that integrates Network Data Envelopment Analysis (NDEA) with a chance-constrained programming. The proposed approach captures the interrelated dynamics of economic production and waste treatment subsystems, while accounting for stochastic variables and data uncertainties to provide robust CE efficiency estimates. Using data from 26 European (EU) countries from 2013 to 2020, our results reveal that achieving CE efficiency requires a balanced focus on economic production and waste management. Although strong economic output can support circularity, waste treatment efficiency often plays a decisive role in determining overall CE performance. Moreover, we find that economic size does not necessarily translate into circular efficiency, whilst large economies may face challenges with effective waste management and resource recovery despite their economic status. The proposed approach offers policymakers and practitioners a robust empirical framework to guide CE improvements, particularly in regions where environmental practices lag behind economic achievements. Stronger incentives and regulatory measures are recommended to enhance circular activities within the EU and foster greater circular efficiency across countries.

Biological data can have complex structures due to the high dependence on genes, limited observations, and sparse interactions. This complexity increases when we also consider the influence of time on the construction of the system. This study proposes a comparative study among the penalized likelihood method and two well-known Bayesian approaches under time chain Gaussian copula graphical model. The underlying Bayesian methods are the birth-death Markov chain Monte Carlo (BDMCMC) and reversible jump MCMC (RJMCMC) algorithms. In the implementation of RJCMCMC, we also propose three types of Bayesian schemes, namely, semi-Bayesia, and full-Bayesian approaches, and modified RJMCMC with adaptive turning parameters to estimate model parameters of near-time network structures. In the comparative analyses, we evaluate the performance of the three approaches by using different simulated datasets, and in the assessment, we compute both specificity and Matthew's correlation coefficient while comparing their accuracy.

Rising income levels and increased consumer awareness have led to a more positive attitude towards insurance, resulting in market expansion and heightened competition. However, businesses must consider factors that could negatively impact insurance demand. One significant factor identified in this study is religion. While some religious texts and teachings advocate for collective mutual assistance, certain religious beliefs view insurance negatively for various reasons. Consequently, this research seeks to explore two critical questions: “How do religious beliefs influence the insurance demands and purchasing behaviors of individuals and societies?” and “What are the potential impacts of economic indices on insurance policy purchases?” Answering these questions requires navigating a complex interplay of economic and cultural factors. To address these objectives, the study utilized data such as per capita insurance expenditures, 66 market totals, and national insurance market shares. The analysis also considered the percentage of the total population covered by national health services, as this coverage might reduce the likelihood of acquiring insurance policies. Statistical analyses were employed to assess the influence of religious beliefs on insurance purchasing behavior and to evaluate the effects of economic indices on insurance policy purchases. The research results revealed that individuals who did not adhere to any specific religious doctrine exhibited the highest rate of insurance purchases. Additionally, the influence of economic indices on insurance purchasing behaviors produced significant and undeniable results. In conclusion, this study highlights the considerable impact of religious beliefs on insurance policy purchasing behavior. The findings contribute valuable insights to the existing literature and offer a contemporary perspective for future research in this field.