Do non-linearity and non-Gaussianity truly matter in streamflow forecasting? A comparative study between PAR(p) and vine copula for Brazilian streamflow time series

This study evaluates the joint impact of non-linearity and non-Gaussianity on predictive performance in 23 Brazilian monthly streamflow time series from 1931 to 2022. We consider point and interval forecasting, employing a PAR(p) model and comparing it with the periodic vine copula model. Results indicate that the Gaussian hypothesis assumed by PAR(p) is unsuitable; gamma and log-normal distributions prove more appropriate and crucial for constructing accurate confidence intervals. This is primarily due to the assumption of the Gaussian distribution, which can lead to the generation of confidence intervals with negative values. Analyzing the estimated copula models, we observed a prevalence of the bivariate Normal copula, indicating that linear dynamic dependence is frequent, and the Rotated Gumbel 180°, which exhibits lower tail dependence. Overall, the temporal dynamics are predominantly shaped by combining these two types of effects. In point forecasting, both models show similar behavior in the estimation set, with slight advantages for the copula model. The copula model performs better during the out-of-sample analysis, particularly for certain power plants. In interval forecasting, the copula model exhibits pronounced superiority, offering a better estimation of quantiles. Consistently demonstrating proficiency in constructing reliable and accurate intervals, the copula model reveals a notable advantage over the PAR(p) model in interval forecasting.

Measuring household vulnerability to medical expenditure shock: method and its empirical application

To investigate household vulnerability for inability to cope with medical expenditure shock, we propose a method of measuring household vulnerability to medical expenditure shock by allowing for the heteroscedasticity and dependence of medical expenditure shock and income shock. Using the data from China Health and Nutrition Survey, we estimate the vulnerability of Chinese households, and further investigate crucial characteristics associated with it by comparing the vulnerability levels among groups with different characteristics and an empirical regression with Shorrocks-Shapely decomposition of R squared. Our research shows that health status contributes most to the household vulnerability, and good health helps to reduce the household's vulnerability. Households with stable income and high-education have greater ability to cope with uncertain medical expenditure, and are less vulnerable. Medical insurance plays a limited role in reducing household vulnerability, and the specific type of medical insurance has little influence. All of these findings are conducive to identifying vulnerable households and designing policies to reduce the vulnerability of households.

Probabilistic monitoring of meteorological drought impacts on water quality of major rivers in South Korea using copula models

The impacts of drought range from water supply for humans to ecosystems. Drought affects river water quality by disturbing the hydrological regime in a variety of ways, and can degrade water quality by reducing surface and groundwater availability. In particular, drought-induced low flows, reduced nutrient dilution, and extreme increases in water temperature affect various water quality parameters in streams. Furthermore, the effects of drought on stream water quality may vary from season to season and from stream segment to stream segment, which requires careful investigation. In this study, Environmental Drought Condition Index - water quality (EDCI-wq) is proposed using a bivariate copula joint probability model between meteorological drought index and river water quality. Using this, environmental drought with respect to water quality is defined, and it is confirmed that environmental drought with respect to water quality can be routinely monitored through time series analysis and mapping of the proposed EDCI-wq. In addition, in order to express the environmental drought condition more explicitly to the general public, the environmental drought condition is graded into four classes based on the EDCI-wq. Furthermore, the sensitivity of river water quality to meteorological drought was estimated using the copula joint probability model, which allowed us to identify river segments that are relatively more sensitive to meteorological drought events.

Beyond a deterministic representation of the temperature dependence of soil respiration

Soil CO2 efflux represents a complex interplay of biological and physical processes that result in the production and transfer of CO2 from soils to the atmosphere. Temperature has been widely recognized as a critical factor regulating soil CO2 efflux and is commonly utilized in deterministic empirical models to predict this important flux for the carbon cycle. This study introduces the Bernstein copula-based cosimulation (BCC) as a data-driven probabilistic approach to model the temperature-soil CO2 efflux relationship. The BCC accounts for the joint probability distribution and temporal dependence of soil CO2 efflux, which are often overlooked in deterministic models. The BCC was implemented as a proof of concept using two years of data on soil CO2 efflux conditioned by soil temperature in a temperate forest. The BBC accurately reproduced the original probability distribution, temporal dependency, and temperature-soil CO2 efflux relationship. Our findings show that a deterministic method, such as the commonly employed exponential relationship between soil CO2 efflux and temperature, is limited for comprehensively capturing the intricate nature of the temperature-soil CO2 efflux relationship. This is due to the confounding and interacting effects of environmental drivers beyond temperature, which are not fully accounted for in such a deterministic approach. Furthermore, the BCC revealed that the probability density between the joint cumulative probability of temperature and soil CO2 efflux is not constant, which raises the concern that deterministic approaches introduce incorrect assumptions for estimating temperature-soil CO2 relationship. In conclusion, we propose that probabilistic approaches hold promise for effectively depicting dependency relationships for soil CO2 efflux modeling, and for improving predictions of the effects of weather variability and climate change.

A simulation and risk assessment framework for water-energy-environment nexus: A case study in the city cluster along the middle reach of the Yangtze River, China

In the Anthropocene, there is a strong interlinkage among water, energy, and the environment. The water-energy-environment nexus (WEEN) has been vigorously advocated as an emerging development paradigm and a global research agenda. Based on the nexus concept, a framework for the WEEN complex system simulation and risk assessment is developed. The three metropolitan areas of the city cluster along the middle reaches of the Yangtze River (CCMRYR) are taken as the objects. Regional policies are combined with generic shared socio-economic pathways (SSPs) to form a localized SSPs suitable for the research region. The dynamic simulation of the WEEN complex system and the risk analysis are carried out with the combination of system dynamics models and copula functions. Results show that: There are obvious differences in water utilization, energy consumption, air pollutant emissions, and water pollutant emissions among the three metropolitan areas. The issue of high carbon intensity in the Wuhan Metropolitan Coordinating Region needs to be emphasized and solved from the perspective of optimizing the industrial structure. Adhering to current development patterns, there will be successive peaks in water utilization, energy consumption, and carbon emissions in Wuhan, Dongting Lake, and Poyang Lake Metropolitan Coordinating Region by 2030, leading to high synergy risks at the systemic level, with maximum values of 0.84, 0.85, 0.62, respectively. A development path based on conservation priorities indicates that future policymaking needs to prioritize a resource-saving and pollution-control development pattern directed by technological upgrading against the backdrop of scarce natural resource endowments. The localized SSPs are a beneficial extension that enriches the narrative of regional-scale SSPs. The evolutionary trajectories and risk assessments of WEEN complex systems under different localized SSPs provide a sweeping insight into the consequences of policy decisions, thus enabling policymakers to appraise policy rationality and implement appropriate corrective measures.

Factorial survival analysis for treatment effects under dependent censoring

Factorial analyses offer a powerful nonparametric means to detect main or interaction effects among multiple treatments. For survival outcomes, for example, from clinical trials, such techniques can be adopted for comparing reasonable quantifications of treatment effects. The key difficulty to solve in survival analysis concerns the proper handling of censoring. So far, all existing factorial analyses for survival data have been developed under the independent censoring assumption, which is too strong for many applications. As a solution, the central aim of this article is to develop new methods for factorial survival analyses under quite general dependent censoring regimes. This will be accomplished by combining existing nonparametric methods for factorial survival analyses with techniques developed for survival copula models. As a result, we will present an appealing F-test that exhibits sound performance in our simulation study. The new methods are illustrated in a real data analysis. We implement the proposed method in an R function surv.factorial(.) in the R package compound.Cox.

Copula based trivariate spatial modeling of childhood illnesses in Western African countries

Acute respiratory infections (ARI), diarrhea, and fever are three common childhood illnesses, especially in sub-Saharan Africa. This study investigates the marginal and pairwise correlated effects of these diseases across Western African countries in a single analytical framework. Using data from nationally representative cross-sectional Demographic and Health Surveys, the study analyzed specific and correlated effects of each pair of childhood morbidity from ARI, diarrhea, and fever using copula regression models in fourteen contiguous Western African countries. Data concerning childhood demographic and socio-economic conditions were used as covariates. In this cross-sectional analysis of 152,125 children aged 0-59 months, the prevalence of ARI was 6.9%, diarrhea, 13.8%, and fever 19.6%. The results showed a positive correlation and geographical variation in the prevalence of the three illnesses across the study region. The estimated correlation and 95% confidence interval between diarrhea and fever is 0.431(0.300,0.539); diarrhea and ARI is 0.270(0.096,0.422); and fever and ARI is 0.502(0.350,0.614). The marginal and correlated spatial random effects reveal within-country spatial dependence. Source of water and access to electricity was significantly associated with any of the three illnesses, while television, birth order, and gender were associated with diarrhea or fever. The place of residence and access to newspapers were associated with fever or ARI. There was an increased likelihood of childhood ARI, diarrhea, and fever, which peaked at about ten months but decreased substantially thereafter. Mother's age was associated with a reduced likelihood of the three illnesses. The maps generated could be resourceful for area-specific policy-making to speed up mitigation processes.

Thresholds for triggering the propagation of meteorological drought to hydrological drought in water-limited regions of China

Propagation thresholds that trigger a transition between meteorological drought and hydrological drought are poorly understood, which hinders effective establishment of drought warning systems and prevention measures. Here, propagation thresholds were assessed by firstly identifying drought events during 1961-2016 in the Yellow River Basin, China, subsequently pooling, excluding, and matching them, and finally assessing their threshold conditions by using a combined Copula function and transition rate (T_r) analysis. These results show that response time changed according to variations in drought duration and watershed characteristics. Importantly, response times increased according to the timescales over which they were studied; for example, the Wenjiachuan watershed recorded response times of 8, 10, 10, and 13 months when examined at 1-, 3-, 6-, and 12-month timescales, respectively. Additionally, the severity and duration of meteorological and hydrological drought events both increased when events were combined rather than studied individually. These effects were also amplified for matched meteorological and hydrological droughts by factors of 1.67 (severity) and 1.45 (duration), respectively. Shorter response times were identified in the Linjiacun (LJC) and Zhangjiashan (ZJS) watersheds, and correlated with their relatively small T_r values of 43 % and 47 %, respectively. Higher propagation thresholds for drought characteristics (e.g., 1.81 and 1.95 for drought severity in the LJC and ZJS watersheds, respectively) imply that shorter response times tended to have greater effects on hydrological drought events and lowered their T_r, and vice versa. These results provide new insight into propagation thresholds used for water resource planning and management, and may help to mitigate the effects of future climate change.

Portfolio value-at-risk estimation for spot chartering decisions under changing trade patterns: A copula approach

Evolving geopolitical relationships between countries (especially between China and the United States) in recent years have highlighted dynamically changing trade patterns across the globe, all of which elevate risk and uncertainty for transport service providers. In order to mitigate risks, shipowners and operators must be able to estimate risks appropriately; one potentially promising method of doing so is through the value-at-risk (VaR) method. VaR describes the worst loss a portfolio is likely to sustain, which will not be exceeded over a target time horizon at a given level of confidence. This article proposes a copula-based GARCH model to estimate the joint multivariate distribution, which is a key component in VaR estimation. We show that the copula model can capture the VaR more successfully, as compared with the traditional method of calculation. As an empirical study, the expected portfolio VaR is examined when a shipowner chooses among Panamax soybean trading routes under a condition of reduced trade volumes between the United States and China due to the ongoing trade turmoil. This study serves as one of the very few papers in the literature on shipping portfolio VaR analysis. The results have significant implications for shipowners regarding fleet repositioning, decision making, and risk management.

Dependence analysis of social contact behaviors under the impacts of COVID-19 based on a copula approach

The spread of the SARS-CoV-2 virus during the COVID-19 pandemic was intricately linked with contact between people, but many of the policies designed to encourage safe contact behaviors were unsuccessful. One reason was that the determinants of social contact decisions have not been thoroughly investigated using scientifically sound methodologies. To fill this gap, a unique survey was designed which sought data on social contact behaviors and their determinants. Second, a copula-based behavior model was developed to jointly represent the choices of contact modes (including direct and indirect contact) and the number of contacted persons. The survey was conducted in six countries from March to May 2021 and collected valid responses from >7000 people. A comparison of five key copula functions found that the Frank function outperformed the others. The results of a Frank-based model showed that indirect contacts were significantly and positively associated with the number of contacted persons. Then the influence of various determinants, including activity attributes (e.g., frequency and travel distance), protective measures, safety level of activity settings, and psychological factors related to activity participation and risk perception, were extensively analyzed. In particular, the various heterogeneous influences in different social contact settings were examined. The findings provide scientific evidence for policymakers to promote safe social distancing, even for the post-pandemic era.

A copula model of extracting DEM-based cross-sections for estimating ecological flow regimes in data-limited deltaic-branched river systems

For operational flood control and estimating ecological flow regimes in deltaic branched-river systems with limited surveyed cross-sections, accurate river stage and discharge estimation using public domain Digital Elevation Model (DEM)-extracted cross-sections are challenging. To estimate the spatiotemporal variability of streamflow and river stage in a deltaic river system using a hydrodynamic model, this study demonstrates a novel copula-based framework to obtain reliable river cross-sections from SRTM (Shuttle Radar Topographic Mission) and ASTER (Advanced Spaceborne Thermal Emission and Reflection) DEMs. Firstly, the accuracy of the CSRTM and CASTER models was assessed against the surveyed river cross-sections. Thereafter, the sensitivity of the copula-based river cross-sections was evaluated by simulating river stage and discharge using MIKE11-HD in a complex deltaic branched-river system (7000 km²) of Eastern India having a network of 19 distributaries. For this, three MIKE11-HD models were developed based on surveyed cross-sections and synthetic cross-sections (CSRTM and CASTER models). The results indicated that the developed Copula-SRTM (CSRTM) and Copula-ASTER (CASTER) models significantly reduce biases (NSE>0.8; IOA>0.9) in the DEM-derived cross-sections and hence, are capable of satisfactorily reproducing observed streamflow regimes and water levels using MIKE11-HD. The performance evaluation metrics and uncertainty analysis indicated that the MIKE11-HD model based on the surveyed cross-sections simulates with higher accuracies (streamflow regimes: NSE>0.81; water levels: NSE>0.70). The MIKE11-HD model based on the CSRTM and CASTER cross-sections, reasonably simulates streamflow regimes (CSRTM: NSE>0.74; CASTER: NSE>0.61) and water levels (CSRTM: NSE>0.54; CASTER: NSE>0.51). Conclusively, the proposed framework is a useful tool for the hydrologic community to derive synthetic river cross-sections from public domain DEMs, and simulate streamflow regimes and water levels under data-scarce conditions. This modelling framework can be easily replicated in other river systems of the world under varying topographic and hydro-climatic conditions.

Application of wastewater-based surveillance and copula time-series model for COVID-19 forecasts

The objective of this study was to develop a novel copula-based time series (CTS) model to forecast COVID-19 cases and trends based on wastewater SARS-CoV-2 viral load and clinical variables. Wastewater samples were collected from wastewater pumping stations in five sewersheds in the City of Chesapeake VA. Wastewater SARS-CoV-2 viral load was measured using reverse transcription droplet digital PCR (RT-ddPCR). The clinical dataset included daily COVID-19 reported cases, hospitalization cases, and death cases. The CTS model development included two steps: an autoregressive moving average (ARMA) model for time series analysis (step I), and an integration of ARMA and a copula function for marginal regression analysis (step II). Poisson and negative binomial marginal probability densities for copula functions were used to determine the forecasting capacity of the CTS model for COVID-19 forecasts in the same geographical area. The dynamic trends predicted by the CTS model were well suited to the trend of the reported cases as the forecasted cases from the CTS model fell within the 99 % confidence interval of the reported cases. Wastewater SARS CoV-2 viral load served as a reliable predictor for forecasting COVID-19 cases. The CTS model provided robust modeling to predict COVID-19 cases.

Semiparametric copula method for semi-competing risks data subject to interval censoring and left truncation: Application to disability in elderly

We aim to evaluate the marginal effects of covariates on time-to-disability in the elderly under the semi-competing risks framework, as death dependently censors disability, not vice versa. It becomes particularly challenging when time-to-disability is subject to interval censoring due to intermittent assessments. A left truncation issue arises when the age time scale is applied. We develop a flexible two-parameter copula-based semiparametric transformation model for semi-competing risks data subject to interval censoring and left truncation. The two-parameter copula quantifies both upper and lower tail dependence between two margins. The semiparametric transformation models incorporate proportional hazards and proportional odds models in both margins. We propose a two-step sieve maximum likelihood estimation procedure and study the sieve estimators' asymptotic properties. Simulations show that the proposed method corrects biases in the marginal method. We demonstrate the proposed method in a large-scale Chinese Longitudinal Healthy Longevity Study and provide new insights into preventing disability in the elderly. The proposed method could be applied to the general semi-competing risks data with intermittently assessed disease status.

Copula-based bivariate count data regression models for simultaneous estimation of crash counts based on severity and number of vehicles

Statistical models of crash frequency typically apply univariate regression models to estimate total crash frequency or crash counts by various categories. However, a possible correlation between the dependent variables or unobserved variables associated with the dependent variables is not considered when univariate models are used to estimate categorized crash counts-such as different severity levels or numbers of vehicles involved. This may lead to inefficient parameter estimates compared to multivariate models that directly consider these correlations. This paper compares the results obtained from univariate negative binomial regression models of property-damage only (PDO) and fatal plus injury (FI) crash frequencies to models using traditional bivariate and copula-based bivariate negative binomial regression models. A similar comparison was made using models for the expected crash frequency of single- (SV) and multi-vehicle (MV) crashes. The models were estimated using two-lane, two-way rural highway segment-level data from an engineering district in Pennsylvania. The results show that all bivariate negative binomial models (with or without copulas) outperformed the corresponding univariate negative binomial models for PDO and FI, as well as SV and MV, crashes. Second, the statistical association of various traffic and roadway/roadside features with PDO and FI, as well as SV and MV crashes, were not the same relative to their corresponding relationships in the univariate models. The bivariate negative binomial model with normal copula outperformed all other models based on the goodness-of-fit statistics. The results suggest that copula-based bivariate negative binomial regression models may be a valuable alternative for univariate models when simultaneously modeling two disaggregate levels of crash counts.

Multivariate models of commodity futures markets: a dynamic copula approach

We apply flexible multivariate dynamic models to capture the dependence structure of various US commodity futures across different sectors between 2004 and 2022; particular attention is paid to the 2008 financial crisis and the COVID-19 pandemic. Our copula-based models allow for time-varying nonlinear and asymmetric dependence by integrating elliptical and skewed copulas with dynamic conditional correlation (DCC) and block dynamic equicorrelation (Block DECO). Flexible copula models that allow for multivariate asymmetry and tail dependence are found to provide the best performance in characterizing co-movements of commodity returns. We also find that the connectedness between commodities has dramatically increased during the financial distress and the COVID-19 pandemic. The impacts of the financial crisis appear to be more persistent than those of the pandemic. We apply our models to some risk management tasks in the commodity markets. Our results suggest that optimal portfolio weights based on dynamic copulas have persistently outperformed the equal-weighted portfolio, demonstrating the practicality and usefulness of our proposed models.

Extreme dependencies and spillovers between gold and stock markets: evidence from MENA countries

This study addresses whether gold exhibits the function of a hedge or safe haven as often referred to in academia. It contributes to the existing literature by (i) revisiting this question for the principal stock markets in the Middle East and North Africa (MENA) region and (ii) using the copula-quantile-on-quantile and conditional value at risk methods to detail the risks facing market participants provided with accurate information about various gold and stock market scenarios (i.e., bear, normal, bull). The results provide strong evidence of quantile dependence between gold and stock returns. Positive correlations are found between MENA gold and stock markets when both are bullish. Conversely, when stock returns are bearish, gold markets show negative correlations with MENA stock markets. The risk spillover from gold to stock markets intensified during the global financial and European crises. Given the risk spillover between gold and stock markets, investors in MENA markets should be careful when considering gold as a safe haven because its effectiveness as a hedge is not the same in all MENA stock markets. Investors and portfolio managers should rebalance their portfolio compositions under various gold and stock market conditions. Overall, such precise insights about the heterogeneous linkages and spillovers between gold and MENA stock returns provide potential input for developing effective hedging strategies and optimal portfolio allocations.

Future global concurrent droughts and their effects on maize yield

Droughts are one of the most devastating natural disasters. Droughts can co-exist in different forms (e.g. meteorological, hydrological, and agricultural) as concurrent droughts. Such concurrent droughts can have far reaching implications for crop yield and global food security. The present study aims to assess global concurrent drought traits and their effects on maize yield under climate change. The standardized indices of precipitation, runoff, and soil moisture incorporated as multivariate standardized drought index (MSDI) using copula functions are used to quantify the concurrent droughts. The ensemble data of several General Circulation Models (GCMs) considering the high emission scenario of Coupled Model Intercomparison Project phase 6 (CMIP6) are utilized. Applying run theory on a time series (1950-2100) of MSDI values, the duration, severity, areal coverage, and average areal intensity of concurrent droughts are computed. The temporal evolution of drought duration and severity are compared among historical (1950-2014), near future (2021-2060), and far future (2061-2100) timeframes. The results indicate that the most vulnerable regions in the late 21st century are Central America, the Mediterranean, Southern Africa, and the Amazon basin. The indices and spatial extent of the individual droughts are used as predictor variables to predict the country-level crop index of the top seven producers of maize. The historical dynamics between maize yield and different drought forms are projected using XGBoost (Extreme Gradient Boosting) algorithms. The future temporal changes in drought-crop yield dynamics are tracked using probabilities of various drought forms under yield-loss conditions. The conditional concurrent drought probabilities are as high as 84 %, 64 %, and 37 % in France, Mexico, and Brazil, revealing that concurrent drought affects the maize yield tremendously in the far future. This approach of applying statistical and soft-computing techniques could aid in drought mitigation under changing climatic conditions.

GC-EnC: A Copula based ensemble of CNNs for malignancy identification in breast histopathology and cytology images

In the present work, we have explored the potential of Copula-based ensemble of CNNs(Convolutional Neural Networks) over individual classifiers for malignancy identification in histopathology and cytology images. The Copula-based model that integrates three best performing CNN architectures, namely, DenseNet-161/201, ResNet-101/34, InceptionNet-V3 is proposed. Also, the limitation of small dataset is circumvented using a Fuzzy template based data augmentation technique that intelligently selects multiple region of interests (ROIs) from an image. The proposed framework of data augmentation amalgamated with the ensemble technique showed a gratifying performance in malignancy prediction surpassing the individual CNN's performance on breast cytology and histopathology datasets. The proposed method has achieved accuracies of 84.37%, 97.32%, 91.67% on the JUCYT, BreakHis and BI datasets respectively. This automated technique will serve as a useful guide to the pathologist in delivering the appropriate diagnostic decision in reduced time and effort. The relevant codes of the proposed ensemble model are publicly available on GitHub.

Gold price and exchange rate in pre and during Covid-19 period in India: Modelling dependence using copulas

This study examines the dynamic relationship between the gold price and the exchange rate in pre- and during Covid-19 pandemic in India. We consider the periods of about equal length for both the pre- and during Covid-19 by considering the data from January 1, 2019 till February 28, 2021. The descriptive analysis shows a significant increase in the dynamics of gold price and exchange rate after mid-March 2020. The results derived from the ARDL approach show a positive and significant relationship between the gold price and exchange rate both in the long and short run. We have selected the best fitted bivariate copula to study the joint distribution of the gold price and the exchange rate. Using the copula model, we examine the relationship between the gold price and exchange rate in a bivariate framework. We have studied the dependence between them including the tail dependencies using the fitted copula. Our findings reveal that the gold price and exchange rate are significantly correlated for the entire study period, and it also reveals that there is no tail dependence. However, the mutual association between the variables is not confirmed in the considered Covid-19 period.

Study on outlier detection method of the near infrared spectroscopy analysis by probability metric

Due to the high dimensionality and non-linearity of the near infrared (NIR) spectra data result the difficulty of the outlier measure. This paper proposed a probability based outlier detection method, which adopted the distribution probability of the spectra data to identify outliers at each wavelength by using of copula function. The negative logarithmic function was also used to quantify the overall variation of the joint distribution for the outliers. This method not only enlarges the difference of the spectra between typical samples and outliers, but also can be adapted to multi-type of outliers. Moreover, the jump degree in statistics was introduced for the automated determination of threshold for the outliers, which avoids the threshold setting problem in empirical way and the misjudgment of the outliers. In order to investigate the effectiveness of the algorithm, the recognition of different cases and types of outliers were applied, and compared with the commonly used PCA-Mahalanobis distance, spectral residual (SR) and leverage methods. The experimental results showed that the probability based outlier detection method effectively improved the performance of outlier identification and calibration for NIR analysis.

Dependence between Chinese stock market and Vietnamese stock market during the Covid-19 pandemic

The study aims to investigate the tail dependence between Chinese stock market and Vietnamese stock market in the context of the Covid-19 pandemic. Using the data on the Ho Chi Minh City Stock Exchange (VNI) and the Shanghai Stock Exchange (SSEC) representing for Vietnam and China stock markets, the study reveals the tail dependence across three periods including: pre-pandemic, during the chaos of the pandemic, and the period of adaptation to the pandemic. Using the copula method including Normal, Clayton, Plackett, Frank, Student, Symmetrised Joe-Clayton copulas, the research results confirm that there is no dependent relationship between the stock market between the two countries in the pre-pandemic. During the pandemic, the Vietnamese stock market is heavily dependent on Chinese stock market, especially the upper tail dependence. During the period of adaptation to the pandemic, this dependence relationship still exists but less than that in the pandemic.

On the targets of inference with multivariate failure time data

There are several different topics that can be addressed with multivariate failure time regression data. Data analysis methods are needed that are suited to each such topic. Specifically, marginal hazard rate models are well suited to the analysis of exposures or treatments in relation to individual failure time outcomes, when failure time dependencies are themselves of little or no interest. On the other hand semiparametric copula models are well suited to analyses where interest focuses primarily on the magnitude of dependencies between failure times. These models overlap with frailty models, that seem best suited to exploring the details of failure time clustering. Recently proposed multivariate marginal hazard methods, on the other hand, are well suited to the exploration of exposures or treatments in relation to single, pairwise, and higher dimensional hazard rates. Here these methods will be briefly described, and the final method will be illustrated using the Women's Health Initiative hormone therapy trial data.

Is CSR linked to idiosyncratic risk? Evidence from the copula approach

In this paper, we extend the research on the effect of corporate social responsibility (CSR) on firm risk by analyzing the CSR-idiosyncratic risk nexus and how CSR can be integrated as insurance in a global risk management strategy. First, the causality between CSR and risk was tested. Second, copulas were estimated to strengthen the existing results on the structure of the dependence between the different dimensions of CSR activities and idiosyncratic risk levels. The empirical analysis was conducted on a sample of 254 European-listed firms over the 2018-2020 period. The main results showed a directional causality effect between CSR and idiosyncratic risk, and the dependences were modeled between CSR and realized idiosyncratic risk. This allows a better understanding of the risk implications of CSR for investors, corporate managers, and policy makers.

A copula-based approach for creating an index of micronutrient intakes at household level in Pakistan

Deficiency of micronutrients is considered as the basic cause of health issues. There are a large number of micronutrients to be considered for good health, which are analyzed separately. However, such analyses involve practical as well as methodological complications and it requires construction of an index representing malnutrition of micronutrients. This study proposes copula methodology to categorize malnutrition of micronutrients at household level by combining the dependence structure of various correlated variables. Data of eleven micronutrients are extracted from HIICS- 2015-16 published by Pakistan -Bureau of Statistics. Seven out of the eleven variables are highly correlated, which are considered to construct the index. These include calcium, iron, iodine, zinc, riboflavin, thiamine and phosphorus intakes per capita at household level. Normal probability distribution is found as the best fit to the sample data of all variables. Gaussian copula function is used to derive multivariate probability distribution by combining univariate marginal probability distribution of each micronutrient. The Multivariate distribution of Gaussian copula model is used to calculate cumulative probabilities, which provide a base to categorize households' malnutrition w.r.t. micronutrients. The results show that 60% households lie in very low or low category of micronutrient intakes, 20% of households fall into medium category while 20% fall into high or very high category of micronutrient consumption. The proposed methodology might be helpful to combine other micronutrients as well as a variety of correlated variables in many other fields having a survey data.

Increased probability and severity of compound dry and hot growing seasons over world's major croplands

Dry and hot extremes are major sources of risk to crop yields, and their impacts are expected to increase under future global warming. The co-occurring dry and hot conditions during crop growing seasons have amplified impacts on crop health that are even larger than the sum of their individual impacts, which may cause crop failure. In this study, we focus on the compound dry and hot growing seasons (hereafter CDHGS) for global wheat, rice, maize and soybean in the period 1951-2020. Total precipitation (TP) and accumulated active temperature (AAT) are used as indicators of overall water stress and heat stress, respectively, at the growing season scale. A copula model is used to construct joint distributions of TP and AAT sequences to investigate the joint behavior of dry and hot conditions during crop growing seasons. Our results indicate that after 1980, the growing seasons of the four crops become drier and more rapidly hotter across the globe, the probability of extreme CDHGS (P(TP ≤ TP₂₅,AAT > AAT₇₅)) increases in more than 80% of global croplands, the severity of CDHGS increases in more than 83% of global croplands, especially in Europe, Central Africa and eastern China. This study provides a global dimension analysis on the changes in compound dry and hot stresses within crops growing seasons in the context of global warming, offering helpful techniques to study the interaction between multi-hazards that occur during crop growth processes, which can effectively contribute to guiding the decision-making processes related to risk reduction and agricultural practices.

A copula model integrating atmospheric moisture demand and supply for vegetation vulnerability mapping

Drought caused by various meteorological factors negatively affects vegetation. Constructing a joint probability distribution between vegetation and drought information may be appropriate to understand the vulnerability of vegetation to drought. In this study, a copula-based trivariate joint probability model is proposed to investigate the effects of various aspects of meteorological drought on vegetation (vegetation drought). Because drought can be caused by insufficient precipitation or excessive evapotranspiration, the meteorological drought risk for vegetation was divided into two aspects (atmospheric moisture supply and moisture demand). The vulnerability of vegetation drought was mapped when two aspects of meteorological drought occurred separately or simultaneously at high spatial resolution using remote sensing data. The results revealed that the response of vegetation was significantly different depending on the climatic stressors. Although the sensitivity of vegetation to each drought condition varied from region to region, it was found that vegetation was more vulnerable to drought caused by atmospheric moisture demand in most regions of Far East Asia. It has also been shown that drought conditions, which overlapped with insufficient precipitation and excessive evapotranspiration, can drive vegetation to a far more lethal level. Meanwhile, through comparison with the existing VTCI, the proposed Normalized Vegetation Temperature Condition Index (nVTCI) was found to be able to more rationally monitor vegetation drought in the Far East Asian region.

A copula model to identify the risk of river water temperature stress for meteorological drought

Drought is a natural phenomenon that can occur in all climatic zones, and is persistent and regionally widespread. Extreme drought caused by climate change can have serious consequences for freshwater ecosystems, which can have significant social and economic impacts. In this study, the effect of meteorological drought on river water temperature was analyzed probabilistically in order to identify the risk of river water temperature stress experienced by the aquatic ecosystem when a meteorological drought occurs. Meteorological drought is divided into a situation in which moisture is insufficiently supplied from the atmosphere and a situation in which the atmosphere requires excessive moisture from the earth's surface. Using the copula theory, a joint probabilistic model between the river water temperature and each meteorological drought caused by two causes is proposed. In order to consider the propagation time from meteorological drought to river water temperature, the optimal time-scale meteorological drought index is adopted through correlation analysis between the meteorological drought index calculated at various time-scales and the river water temperature. The optimal copula function of the drought index and river water temperature is determined using AIC analysis. Using the proposed model, a risk map is drawn for the river water temperature stress experienced by the aquatic ecosystem under the user-defined meteorological drought severity. The risk map identifies the stream sections where the river water temperature is relatively more sensitive to meteorological drought. The identified stream sections appear differently depending on the cause of the meteorological drought, the region, and the season.

COVID-19 and currency dependences: Empirical evidence from BRICS

The COVID-19 has caused dramatic fluctuations in international financial markets. This paper tests the effect of this pandemic on foreign exchange dependences within the BRICS economies. Upon dividing the COVID-19 episode into four stages, we document negative effects of the COVID-19 on dependences between CNY and other currencies in the BRICS across different stages. In addition, USD flows positively affect the dependencies of BRL-CNY, INR-CNY, and RUB-CNY pairs in response to the transition of the pandemic stages.

Copula-based framework for integrated evaluation of water quality and quantity: A case study of Yihe River, China

Water quantity and quality are two key factors affecting the performance of integrated watershed management. Conventional water resources assessment of rivers often deals with water quantity and quality separately. However, how to make an objective and impartial assessment of water resources by incorporating both water quantity and quality remains unclear, especially in watersheds with significant human activity impacts and high spatiotemporal variations in flows. In such areas, the nonmonotonic relationship between the water quality and discharge rate of a river, in contrast to near-natural conditions, is often ignored. To resolve this problem, this paper develops a new framework for the integrated evaluation of water quantity and quality by incorporating a new index, namely, the water quality improvement degree (WQID). The WQID is proposed to quantify the disturbance degree of human activities to the near-natural relationship between the water quality and discharge rate of a river. The Yihe River in Northern China is selected as a case study to apply the proposed framework. The results show that the observed flow discharge rates of some abnormal months after a specific time of change-point are greater than the estimated discharges under the river's near-natural condition. The WQID values in these abnormal months are less than 1, resulting in a decrease in the modified water resources surplus (WRS*) or an increase in the modified water resources deficit (WRD*). This indicates that the WQID can take into account the near-natural law between water quantity and quality to make a more objective evaluation of integrated water resources management for the months of interest. The proposed framework can serve as a useful and reliable tool for a comprehensive assessment of the watershed management performance of a river system.

Bayesian Copula Density Deconvolution for Zero-Inflated Data in Nutritional Epidemiology

Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hour recalls of the intakes, which show marked patterns of conditional heteroscedasticity. Significantly compounding the challenges, the recalls for episodically consumed dietary components also include exact zeros. The problem of estimating the density of the latent long-time intakes from their observed measurement error contaminated proxies is then a problem of deconvolution of densities with zero-inflated data. We propose a Bayesian semiparametric solution to the problem, building on a novel hierarchical latent variable framework that translates the problem to one involving continuous surrogates only. Crucial to accommodating important aspects of the problem, we then design a copula based approach to model the involved joint distributions, adopting different modeling strategies for the marginals of the different dietary components. We design efficient Markov chain Monte Carlo algorithms for posterior inference and illustrate the efficacy of the proposed method through simulation experiments. Applied to our motivating nutritional epidemiology problems, compared to other approaches, our method provides more realistic estimates of the consumption patterns of episodically consumed dietary components.

Shared parameter and copula models for analysis of semicontinuous longitudinal data with nonrandom dropout and informative censoring

Analysis of longitudinal semicontinuous data characterized by subjects' attrition triggered by nonrandom dropout is complex and requires accounting for the within-subject correlation, and modeling of the dropout process. While methods that address the within-subject correlation and missing data are available, approaches that incorporate the nonrandom dropout, also referred to informative right censoring, in the modeling step are scarce due to the computational intensity and possible intractable integration needed for its implementation. Appreciating the complexity of this problem and the need for a new methodology that is feasible for implementation, we propose to extend a framework of likelihood-based marginalized two-part models to account for informative right censoring. The censoring process is modeled using two approaches: (1) Poisson censoring for the count of visits before dropout and (2) survival time to dropout. Novel consideration was given to the proposed joint modeling approaches for the semicontinuous and censoring components of the likelihood function which included (1) shared parameter, and (2) Clayton copula. The cross-part and within-part correlations were accounted for through a complex random effect structure that models correlated random intercepts and slopes. Feasibility of implementation, and accuracy of these approaches were investigated using extensive simulation studies and clinical application.

Copula based post-processing for improving the NMME precipitation forecasts

Using reliable and timely precipitation forecasts on a monthly or seasonal scale could be useful in many water resources management planning, especially in countries facing drought challenges. Amongst many, the North American Multi-Model Ensemble (NMME) is one of the most well-known models. In this study, a Bayesian method based on Copula functions has been applied to improve NMME precipitation forecasts. This method is based on the existence of a correlation between the raw forecast and observational data. Two main factors affect the results of rainfall improvement based on the selected method. This research has presented innovative methods in these regards namely; 1) the approach of selecting the appropriate statistical distribution for variables and 2) the selection method of improved data according to the conditional probability distribution functions (CPDF). To evaluate the effectiveness of the statistical distribution, firstly the precipitation forecast improvement model has been developed based on the application of parametric (Exponential, Normal, Gamma, LogNormal and General Exreteme Value (GEV)) and non-parametric distributions (Standard Normal Kernel). Then the novel mixed distribution function based on GEV parametric distribution and Standard Normal Kernel (non-parametric distribution) has been suggested. As the second aim, a new method for selecting improved data based on the center of mass of estimated CPDF is presented. The evaluation of the proposed method for estimating the statistical distribution of data and improving the forecast precipitation by the NMME model has been performed in Sistan and Baluchestan province in Iran. In this regard, the data of 1982–2010 for the calibration period and the data of 2012–2016 for the validation of the results have been used. According to the results, the non-parametric distribution best fitted with the data in the time series and selecting the appropriate bandwidth increased the efficiency of this distribution. Besides, due to the weakness of non-parametric distributions in the boundaries, the use of GEV distribution with a high ability to estimate boundary conditions as semi-parametric distribution, led to improved performance of the proposed distribution. Finally, the selection of the improved data based on the center of the mass method has efficiently provided much improvement compared to the maximum likelihood method commonly used.

Modeling asset allocations and a new portfolio performance score

We discuss and extend a powerful, geometric framework to represent the set of portfolios, which identifies the space of asset allocations with the points lying in a convex polytope. Based on this viewpoint, we survey certain state-of-the-art tools from geometric and statistical computing to handle important and difficult problems in digital finance. Although our tools are quite general, in this paper, we focus on two specific questions. The first concerns crisis detection, which is of prime interest for the public in general and for policy makers in particular because of the significant impact that crises have on the economy. Certain features in stock markets lead to this type of anomaly detection: Given the assets’ returns, we describe the relationship between portfolios’ return and volatility by means of a copula, without making any assumption on investors’ strategies. We examine a recent method relying on copulae to construct an appropriate indicator that allows us to automate crisis detection. On real data the indicator detects all past crashes in the cryptocurrency market and from the DJ600-Europe index, from 1990 to 2008, the indicator identifies correctly 4 crises and issues one false positive for which we offer an explanation. Our second contribution is to introduce an original computational framework to model asset allocation strategies, which is of independent interest for digital finance and its applications. Our approach addresses the crucial question of evaluating portfolio management, and is relevant the individual managers as well as financial institutions. To evaluate portfolio performance, we provide a new portfolio score, based on the aforementioned framework and concepts. In particular, it relies on statistical properties of portfolios, and we show how they can be computed efficiently.

Spatial contagion between financial markets: new evidence of asymmetric measures

The objective of this paper is to identify the presence, direction and time at which the pure contagion effect occurred between financial markets. In so doing, the aim is to prove the existence of both spatial and temporal asymmetries of pure contagion effects. Firstly, a new empirical framework is proposed in order to define a spatial contagion index using the conditional cumulative distribution function as a parameter to estimate a conditional copula. This methodology enables us to estimate a dynamic conditional copula, providing information about how the market sent pure contagion effects and when. Secondly, in addition to detecting the direction of contagion, the real-time contagion effect is determined, enabling us to calculate the delay of contagion effects (spillover) between financial markets. The present empirical results show the existence of both spatial and temporal asymmetry for bilateral contagion effects for 16 mature and emerging stock markets during the 2001-2018 period. This proves the importance of taking temporal asymmetry into account when we want to detect the contagion effect of every crisis and to estimate the period of pure contagion relating to investors' behaviors. Finally, these findings highlight the fact that contagion effects were more intensive during the subprime crisis than they were during the European debt crisis.

[Multiple-scale intermuscular coupling network analysis]

In order to more accurately and effectively understand the intermuscular coupling of different temporal and spatial levels from the perspective of complex networks, a new multi-scale intermuscular coupling network analysis method was proposed in this paper. The multivariate variational modal decomposition (MVMD) and Copula mutual information (Copula MI) were combined to construct an intermuscular coupling network model based on MVMD-Copula MI, and the characteristics of intermuscular coupling of multiple muscles of upper limbs in different time-frequency scales during reaching exercise in healthy subjects were analyzed by using the network parameters such as node strength and clustering coefficient. The experimental results showed that there are obvious differences in the characteristics of intermuscular coupling in the six time-frequency scales. Specifically, the triceps brachii (TB) had relatively high coupling strength with the middle deltoid (MD) and posterior deltoid (PD), and the intermuscular function was closely connected. However, the biceps brachii (BB) was independent of other muscles. The intermuscular coupling network had scale differences. MVMD-Copula MI can quantitatively describe the relationship of multi-scale intermuscular coupling strength, which has good application prospects.

Early warning of water quality degradation: A copula-based Bayesian network model for highly efficient water quality risk assessment

In the context of global climate change and increasingly severe environmental pollution, drinking water quality risk assessments to provide crucial early warnings have become essential routine work. At present, traditional water quality assessment methods are commonly used without considering the correlation among different indicators and the substantial uncertainty from multiple sources, which limit their applications. To address this issue, a copula-based Bayesian network (CBN) method was proposed in this study to concretely evaluate the water quality risk with multiple environmental risk indicators in a large drinking water reservoir in Tianjin city, China. Taking rainfall and water temperature (WT) as external environmental risk indicators and pH, ammonia nitrogen (NH₃-N), total nitrogen (TN), total phosphorus (TP), and permanganate index (COD_Mn) as internal environmental risk indicators, the CBN model was constructed to investigate the interaction between the indicators and water quality state and assess the contingent risk. Our results showed that TN and NH₃-N should be considered key risk indicators. Additionally, we performed forward and backward risk analyses to assess water quality risk during different seasons and determined the distributions of key indicators under different water quality risk grades. From a time perspective, the reservoir's water quality risk is much higher in winter and spring than in other seasons affected by winter snowfall. From a spatial perspective, the water quality risk is much higher at the reservoir's entrance than at other locations affected by water diversion. Furthermore, we found that the probability of water quality risk events may be relatively high when the TN concentration is 3.6 mg/L to 6.4 mg/L at the reservoir's entrance. The results reveal that the CBN method could be an invaluable decision-support tool for reservoir managers and scientists, which could provide an early warning of water quality degradation by only inputting monitoring data.

Singleton or twin male lambs: Effects on their reproductive development

Because intrauterine environment differs between twins and singletons, twin-born lambs are often studied when effects of fetal programming are evaluated. In sheep, fetal programming might have effects on reproductive physiology and behavior after sexual maturation. The aim of this study was to compare sperm output and sexual behavior in developing singleton- or twin-born lambs of similar body weight. Singleton lambs (n = 12) and twin (n = 9) male-male lambs were used. From 5.4 until 9.1 months of age, body weight, scrotal circumference (every 3-4 weeks), sexual behavior (every 14 days) and semen characteristics (every 28 days) were evaluated. In the third ejaculate, singleton lambs ejaculated a larger volume of semen than twins (P = 0.03). Considering a pool of the three ejaculates, twin lambs ejaculated semen with a greater sperm concentration than singleton lambs (P = 0.015). There was an interaction between group and time to the onset of courtship behavior (P = 0.02) and a tendency for an interaction in the number of mount attempts (P = 0.052). Singleton-born lambs, during the first evaluation period began courtship behavior earlier than twin-born lambs (P < 0.0001). In conclusion, there were only slight differences in semen and sexual behavior between male ram lambs born as singletons or twins with similar weight. Male ram lambs born as singletons initiated the courtship behavior earlier than twins during the first sexual behavioral evaluation period, ejaculated a larger volume of semen in the third consecutive ejaculate, and there was a lesser sperm concentration in the three ejaculates.

Using the geometric average hazard ratio in sample size calculation for time-to-event data with composite endpoints

Background

Sample size calculation is a key point in the design of a randomized controlled trial. With time-to-event outcomes, it’s often based on the logrank test. We provide a sample size calculation method for a composite endpoint (CE) based on the geometric average hazard ratio (gAHR) in case the proportional hazards assumption can be assumed to hold for the components, but not for the CE.

Methods

The required number of events, sample size and power formulae are based on the non-centrality parameter of the logrank test under the alternative hypothesis which is a function of the gAHR. We use the web platform, CompARE, for the sample size computations. A simulation study evaluates the empirical power of the logrank test for the CE based on the sample size in terms of the gAHR. We consider different values of the component hazard ratios, the probabilities of observing the events in the control group and the degrees of association between the components. We illustrate the sample size computations using two published randomized controlled trials. Their primary CEs are, respectively, progression-free survival (time to progression of disease or death) and the composite of bacteriologically confirmed treatment failure or Staphylococcus aureus related death by 12 weeks.

Results

For a target power of 0.80, the simulation study provided mean (± SE) empirical powers equal to 0.799 (±0.004) and 0.798 (±0.004) in the exponential and non-exponential settings, respectively. The power was attained in more than 95% of the simulated scenarios and was always above 0.78, regardless of compliance with the proportional-hazard assumption.

Conclusions

The geometric average hazard ratio as an effect measure for a composite endpoint has a meaningful interpretation in the case of non-proportional hazards. Furthermore it is the natural effect measure when using the logrank test to compare the hazard rates of two groups and should be used instead of the standard hazard ratio.

Impacts of COVID-19 outbreak on the spillovers between US and Chinese stock sectors

This paper examines the impacts of COVID-19 outbreak on the spillover between ten US and Chinese equity sectors. We use Copula and Conditional Value at Risk approaches. The results show evidence of asymmetric tail dependence during the COVID-19 outbreak with the exception of the Utilities sector, where a symmetric tail dependence is found. Moreover, we find time-varying bidirectional asymmetric risk spillovers from the US to China and vice versa. The risk spillover is higher from the US to China before COVID-19 and from China to the US during COVD-19 spread, which is significantly intensified between March 2020 and April 2020.

Sustainability assessment approaches based on water-energy Nexus: Fictions and nonfictions about non-conventional water resources

In arid and semi-arid regions of the world, non-conventional water resources are considered as alternative water resources and a long-term rescue plan against severe water scarcity. To avoid negative impacts, some criteria and indices are required to justify the extent of this utilization. Production of non-conventional waters requires energy while consumption of energy implies various financial and environmental impacts. In this study, Relative Sustainability Probability has been estimated by "Sandoval-Solis" and "Multivariate Copula" approaches to shed light on fictions and nonfiction of non-conventional water resources. The proposed method has been implemented in the Kashan catchment in central Iran. Results indicate that the "Multivariate Copula" approach is generating the same results as the "Sandoval-Solis" approach but relatively much easier and much faster. Moreover, the proposed method could be inspiringly promoted to higher dimensions of Copula leading to more precise results in complex human-environment systems. Besides this, results are verifying non-conventional water fictions could not be considered as long term sustainable rescue attempts, particularly so in the case of seawater conveyance. Rethinking of sustainability definition should be considered in futuristic policy makings leading to a shift to untypical development scenarios, such as Halo-Engineering concept, insisting on lower water and energy consumption in arid and semi-arid regions.

Studying the properties of the Bitcoin as a diversifying and hedging asset through a copula analysis: Constant and time-varying

In this study, we analyze the properties of Bitcoin as a diversifier asset and hedge asset against the movement of international market stock indices: S&P500 (US), STOXX50 (EU), NIKKEI (Japan), CSI300 (Shanghai), and HSI (Hong Kong). For this, we use several copula models: Gaussian, Student-t, Clayton, Gumbel, and Frank. The analysis period runs from August 18, 2011 to June 31, 2019. We found that the Gaussian and Student-t copulas are best at fitting the structure dependence between markets. Also, these copulas suggest that under normal market conditions, Bitcoin might act as a hedge asset against the stock price movements of all international markets analyzed. However, the dependence on the Shanghai and Hong Kong markets was somewhat higher. Also, under extreme market conditions, the role of Bitcoin might change from hedge to diversifier. In a time-varying copula analysis, given by the Student-t copula, we found that even under normal market conditions, for some markets, the role of Bitcoin as a hedge asset might fail on a high number of days.

Changes in spatiotemporal drought characteristics over northeast China from 1960 to 2018 based on the modified nested Copula model

Drought forecasting is helpful for understanding the inherent mechanism of hydrological extremes and taking corresponding measures to mitigate drought impacts. Northeast China, which is an important, major grain-producing area in China, has been challenged by substantial losses due to frequent drought. In this study, to predict the spatiotemporal variation in drought events over Northeast China, a model-based simulation framework is proposed based on precipitation data at 70 meteorological stations from 1960 to 2018. The core of the model framework is run theory, modified Copula model- based Bayesian-MCMC, Gibbs sampling, and a new definition of drought intensity center and drought intensity accumulation area. The results showed that a total of 6408 drought events occurred at the 70 meteorological stations in Northeast China over the past 59 years. The empirical distribution functions of longitude, latitude, and time can be used to fit the edge distribution of the original variable. In comparison to the traditional maximum likelihood method, the Bayesian-MCMC method is more accurate for parameter estimation of the Copula model. The Frank Copula is the optimum joint function of longitude and latitude, while the Gaussian Copula is the optimum joint function of location and time. Gibbs sampling can provide a relatively larger sample size for predicting future drought conditions. The spatiotemporal variation in drought in Northeast China changes similarly throughout the year. Drought is mainly concentrated in southwestern Liaoning from February to April. The drought intensity center moves to the northeast from May to September. Western Heilongjiang is the main drought-stricken area from October to November. The drought intensity center moves southwest from December to January of the following year. This study provides a method for effectively predicting drought events and is of great significance to the protection, development, and utilization of water resources.

A copula-based approach for jointly modeling crash severity and number of vehicles involved in express bus crashes on expressways considering temporal stability of data

The consequences of crashes, including injury, loss of lives, and damage to properties, are further worsened when buses plying expressways are involved in the crash. Previous studies have separately analyzed crash severity in terms of monetary cost, injuries and loss of lives, and the size of crashes in terms of the number of vehicles involved. However, as both outcome variables are correlated, it is imperative to perform a combined analysis using an appropriate econometric model to achieve a better model fit. This study contributes to the literature by jointly exploring the factors influencing the severity and size of express bus-involved crashes that occur on expressways and characterizes the dependence between both outcome variables by employing a more plausible copula regression framework. Likelihood ratio tests were also conducted to investigate the temporal stability of the factors that affect both crash severity and size. Based on the goodness-of-fit statistics, the Frank copula model proved superior to the independent ordered probit model. The estimate of the underlying dependence between the outcome variables provided a better comprehension of the correlation between them. Temporal instability was detected for the individual parameters in the models and is attributed to the changing driving behavior due to the heightened road safety campaigns. The results suggest that traffic exposure measures are significantly associated with a higher propensity of observing increased bus crash severity and size. Insights into the factors influencing the size and severity of express bus crashes are discussed, and appropriate engineering, enforcement, and education-related countermeasures are proposed.

Dynamic functional connectivity analysis based on time-varying partial correlation with a copula-DCC-GARCH model

We suggest a time-varying partial correlation as a statistical measure of dynamic functional connectivity (dFC) in the human brain. Traditional statistical models often assume specific distributions on the measured data such as the Gaussian distribution, which prohibits their application to neuroimaging data analysis. First, we use the copula-based dynamic conditional correlation (DCC), which does not rely on a specific distribution assumption, for estimating time-varying correlation between regions-of-interest (ROIs) of the human brain. Then, we suggest a time-varying partial correlation based on the Gaussian copula-DCC-GARCH model as an effective method for measuring dFC in the human brain. A recursive algorithm is explained for computation of the time-varying partial correlation. Numerical simulation results demonstrate effectiveness of the partial correlation-based methods against pairwise correlation-based methods. In addition, a two-step procedure is described for the inference of sparse dFC structure using functional magnetic resonance imaging (fMRI) data. We illustrate the proposed method by analyzing an fMRI data set of human participants watching a Pixar animated movie. Based on twelve a priori selected brain regions in the cortex, we demonstrate that the proposed method is effective for inferring sparse dFC network structures and robust to noise distribution and a preprocessing step of fMRI data.

The effects of within-neuron degree correlations in networks of spiking neurons

We consider the effects of correlations between the in- and out-degrees of individual neurons on the dynamics of a network of neurons. By using theta neurons, we can derive a set of coupled differential equations for the expected dynamics of neurons with the same in-degree. A Gaussian copula is used to introduce correlations between a neuron's in- and out-degree, and numerical bifurcation analysis is used determine the effects of these correlations on the network's dynamics. For excitatory coupling, we find that inducing positive correlations has a similar effect to increasing the coupling strength between neurons, while for inhibitory coupling it has the opposite effect. We also determine the propensity of various two- and three-neuron motifs to occur as correlations are varied and give a plausible explanation for the observed changes in dynamics.

A factorial Bayesian copula framework for partitioning uncertainties in multivariate risk inference

In this study, a factorial Bayesian copula (FBC) method is proposed to quantify parameter uncertainties in copula-based models and then reveal their impacts on hydrologic risk inferences within a multivariate context. In detail, Bayesian inference and factorial analysis are integrated into copula-based multivariate risk models to (1) quantify parameter uncertainties, (ii) reveal their individual and interactive effects, and (iii) identify their detailed contributions to uncertain risk inferences. Streamflow observations at Xiangxi and Wei River basins is China are used to illustrate the applicability of FBC. The results indicate that imprecise parameters in marginal distributions and the dependence structure would lead to extensive uncertainties in predictive joint return periods and failure probabilities. Also, individual and interactive effects of parameters are well revealed through multilevel factorial analysis, and the detailed contributions of one parameter to different failure probabilities under different service time scenarios are identified.

System modeling oriented time-delay estimation

Training models to approximate target systems is the dominant method applied to unknown-structure delay system modeling. Due to limited learning ability of the models, the time-delay estimation (TDE) process should be executed prior to the training. The TDE for unknown-structure multi-input multi-output (MIMO) delay systems remains a challenge due to the physical interaction within the system the correlations among the system inputs and outputs. This paper addresses the TDE problem of unknown-structure MIMO delay systems. A dependence measure employed from copula theory, which is named C-dependence, is introduced to measure the dependence among the system inputs and outputs. The relationship between the C-dependence and the time-delays is studied, and the time-delays are estimated by maximizing the C-dependence. The highlight of the proposed method is that no prior decoupling process and system structure are required during the TDE process. Simulation and real data experiments are provided to demonstrate the effectiveness of the proposed method.

Probabilistic hazard assessment of contaminated sediment in rivers

We propose a probabilistic framework rooted in multivariate and copula theory to assess heavy metal hazard associated with contaminated sediment in freshwater rivers that provide crucial ecosystem services such as municipal water source, eco-tourism, and agricultural irrigation. Exploiting the dependence structure between suspended sediment concentration (SSC) and different heavy metals, we estimate the hazard probability associated with each heavy metal at different SSC levels. We derive these relationships for warm (spring-summer) and cold (fall-winter) seasons, as well as stormflow condition, to unpack their nonlinear associations under different environmental conditions. To demonstrate its efficacy, we apply our proposed generic framework to Fountain Creek, CO, and show heavy metal concentration in warm season and under stormflow condition bears a higher hazard likelihood compared to the cold season. Under both warm season and stormflow conditions, probability of exceeding maximum allowable threshold for all studied heavy metals (Cu, Zn, and Pb, in recoverable form) at a standard hardness of 100 mg/lCaCo₃ and at a high level of SSC (95th percentile) is consistently more than 80% in our study site. Moreover, a longitudinal study along the Fountain Creek demonstrates that urban and agricultural land use considerably increase likelihoods of violating water quality standards compared to natural land cover. The novelty of this study lies in introducing a probabilistic hazard assessment framework that enables robust risk assessment with important policy implications about the likelihood of different heavy metals violating water quality standards under various SSC levels.

Assessing multi-risk characteristics of heat and cold stress for rice across the southern parts of China

Rice (Oryza sativa) growth is always threatened by heat as well as cold stress, when it is exposed to natural environment. Heat growing degree hours (HGDH) and cold growing degree hours (CGDH1 and CGDH2) were firstly proposed to quantify heat and cold stress occurred during different growing stages. Information diffusion method was effectively used to fit the distribution and estimate probability of single stress at each station, with an advantage of no limitation in data series. In terms of single stress, highest probability was seen in HGDH, followed by CGDH1 and CGDH2. Seven copula functions, i.e., normal and t, Gumbel-Hougaard, Clayton, Frank, Joe, and Ali-Mikhail-Haq, were applied to fit the distribution of multi-stress with significant dependence, and simple calculation based on single stress was used to quantify the probability for multi-stress with independence. In these copulas, t was the most chosen one in the fitting of HGDH-CGDH1, HGDH-CGDH2, CGDH1-CGDH2, and HGDH-CGDH1-CGDH2, selected by the statistic of Akaike information criterion. Regarding bi-stress, higher joint probability was in HGDH-CGDH1, relative to HGDH-CGDH2 and CGDH1-CGDH2. As expected, the co-occurrence probability of tri-stress was lower than that of bi-stress in the magnitude and spatial extent, while joint probability of tri-stress was larger. Given the condition of occurrence of HGDH or CGDH1, the joint probability of HGDH-CGDH1 was higher than other pairs of bi-stress and tri-stress. It was special that higher joint probability of CGDH1-CGDH2 was detected under the condition of CGDH2 relative to CGDH1. Joint probability of tri-stress was lower under the condition of HGDH-CGDH1, in comparison with HGDH-CGDH2 and CGDH1-CGDH2. Hazards of single stress and multi-stress were expressed by the integration of intensity of stress index and corresponding probability. Most consistent conclusions agreed that central Fujian, Zhejiang, and northeastern Jiangxi were exposed to higher hazard, derived from not only single stress but also multi-stress. These results can be helpful in provision of information regarding prevention and adaptation strategies for rice cultivation as a response to extreme temperature stress.

Patient-specific Conditional Joint Models of Shape, Image Features and Clinical Indicators

We propose and demonstrate a joint model of anatomical shapes, image features and clinical indicators for statistical shape modeling and medical image analysis. The key idea is to employ a copula model to separate the joint dependency structure from the marginal distributions of variables of interest. This separation provides flexibility on the assumptions made during the modeling process. The proposed method can handle binary, discrete, ordinal and continuous variables. We demonstrate a simple and efficient way to include binary, discrete and ordinal variables into the modeling. We build Bayesian conditional models based on observed partial clinical indicators, features or shape based on Gaussian processes capturing the dependency structure. We apply the proposed method on a stroke dataset to jointly model the shape of the lateral ventricles, the spatial distribution of the white matter hyperintensity associated with periventricular white matter disease, and clinical indicators. The proposed method yields interpretable joint models for data exploration and patient-specific statistical shape models for medical image analysis.