A new mixture copula model for spatially correlated multiple variables with an environmental application

This study assesses univariate and multivariate spatial regression models for predicting individual tree structure variables using Light Detection And Ranging (LiDAR) covariates. Many studies have used covariates derived from LiDAR to help explain the variability in tree, stand, or forest variables at a fine spatial resolution across a specified domain. Few studies use regression models capable of accommodating residual spatial dependence between field measurements. Failure to acknowledge this spatial dependence can result in biased and perhaps misleading inference about the importance of LiDAR covariates and erroneous prediction. Accommodating residual spatial dependence, via spatial random effects, helps to meet basic model assumptions and, as illustrated in this study, can improve model fit and prediction. When multiple correlated tree structure variables are considered, it is attractive to specify joint models that are able to estimate the within tree covariance structure and use it for subsequent prediction for unmeasured trees. We capture within tree residual covariances by specifying a model with multivariate spatial random effects. The univariate and multivariate spatial random effects models are compared to those without random effects using a data set collected on the U.S. Forest Service Penobscot Experimental Forest, Maine. These data comprise individual tree measurements including geographic position, height, average crown length, average crown radius, and diameter at breast height.

Modeling the multivariate dynamic dependence structure of commodity futures portfolios

The Multivariate Spatial Durbin Model (MSDM) is a significant advance in spatial econometrics, very relevant in the context of research problems. This model extends spatial analysis by capturing the complexity and dynamism of interactions between variables in a spatial context that is often ignored by classical spatial models. Furthermore, this article aims to estimate the parameters of MSDM model applied to large and complex data sets through Monte Carlo simulations. This model was then estimated using Maximum Likelihood Estimation (MLE), and to test the accuracy of the model using the Maximum Likelihood Ratio Test (MLRT) with a computational approach. The research results show that the MSDM model para-meter estimates are accurate as indicated by an accuracy value that is smaller than the 5% significance level. The model becomes more efficient as the sample size increases.

Financial data usually have the features of complexity and interdependence structure, such as asymmetric, tail, and time-varying dependence. This study constructs a new multivariate skewed fat-tailed copula, namely, noncentral contaminated normal (NCCN) copula, to analyze the dependent structure of financial market data. The dynamic conditional correlation (DCC) model is also incorporated into constructing the time-varying NCCN copula model. This study comprehensively examines the effects of the DCC-NCCN copula and related models on fitting dependence structures of Hong Kong stock markets. The results show that the DCC-NCCN copula model can better depict the dependence structures of returns. Considering the flexibility and complexity, the DCC-NCCN copula model is a relatively ideal, time-varying, multivariate skewed fat-tailed copula model.

We propose a statistical downscaling method to produce fine-resolution climate projections. A multivariate spatial statistical model is developed to jointly analyse high-resolution remote sensing data and coarse-resolution climate model outputs. With a basis function representation, the resulting model can achieve efficient computation and describe potentially nonstationary spatial dependence. We implement our method to produce downscaled sea surface temperature projections over the Great Barrier Reef region from CMIP6 Earth system models. Compared with the state of the art, our method reduces the mean squared predictive error substantially and produces a predictive distribution enabling holistic uncertainty quantification analyses.

. In this article, we focus on the model specification problem in multivariate spatial econometric models when a candidate set for the spatial weights matrix is available. We propose a model selection method for the multivariate spatial autoregressive model when the true spatial weights matrix may not be in the candidates. We show that the selected estimator is asymptotically optimal in the sense of minimizing the squared loss. If the candidate set contains the true spatial weights matrix, the method has selection consistency. We further propose a model averaging estimator that combines a set of candidate models and show its asymptotic optimality. Monte Carlo simulation results indicate that the proposed model selection and model averaging estimators perform quite well in finite samples. The proposed methods are applied to a Sina Weibo data to reveal how the user’s posting behavior is influenced by the users that he follows. The analysis results indicate that the influence tends to be uniformly distributed among the user’s followee, or linearly correlated with the number of followers of the followee.

The Islamic Republic of Iran reported its first COVID-19 cases by 19th February 2020, since then it has become one of the most affected countries, with more than 73,000 cases and 4,585 deaths to this date. Spatial modeling could be used to approach an understanding of structural and sociodemographic factors that have impacted COVID-19 spread at a province-level in Iran. Therefore, in the present paper, we developed a spatial statistical approach to describe how COVID-19 cases are spatially distributed and to identify significant spatial clusters of cases and how socioeconomic and climatic features of Iranian provinces might predict the number of cases. The analyses are applied to cumulative cases of the disease from February 19th to March 18th. They correspond to obtaining maps associated with quartiles for rates of COVID-19 cases smoothed through a Bayesian technique and relative risks, the calculation of global (Moran's I) and local indicators of spatial autocorrelation (LISA), both univariate and bivariate, to derive significant clustering, and the fit of a multivariate spatial lag model considering a set of variables potentially affecting the presence of the disease. We identified a cluster of provinces with significantly higher rates of COVID-19 cases around Tehran (p-value< 0.05), indicating that the COVID-19 spread within Iran was spatially correlated. Urbanized, highly connected provinces with older population structures and higher average temperatures were the most susceptible to present a higher number of COVID-19 cases (p-value < 0.05). Interestingly, literacy is a factor that is associated with a decrease in the number of cases (p-value < 0.05), which might be directly related to health literacy and compliance with public health measures. These features indicate that social distancing, protecting older adults, and vulnerable populations, as well as promoting health literacy, might be useful to reduce SARS-CoV-2 spread in Iran. One limitation of our analysis is that the most updated information we found concerning socioeconomic and climatic features is not for 2020, or even for a same year, so that the obtained associations should be interpreted with caution. Our approach could be applied to model COVID-19 outbreaks in other countries with similar characteristics or in case of an upturn in COVID-19 within Iran.

Multivariate analysis helps to understand the relationships between dependent variables; this methodology has great potential in several areas of knowledge. The aim of this study was to adjust and compare the univariate and multivariate Gompertz and Logistic nonlinear models to describe the productive traits of sunn hemp (Crotalaria juncea L.). Two uniformity trials were performed, and the following productive traits were analyzed in 376 sunn hemp plants along 94 days of observations (four plants per day): the fresh mass of leaves (FML), the fresh mass of stem (FMS), and the fresh mass of the aerial parts (FMAP). The Gompertz and Logistic univariate models were adjusted for each productive trait. To adjust the multivariate models, the errors covariance matrix was calculated. The matrix (Cholesky factor) was obtained for each trait, and the multivariate Gompertz (GG) and Logistic (LL) nonlinear models were generated, together with the combination of both models (GL and LG). To define the best model, the residual standard deviation (RSD), the determination coefficient (R2), the Akaike information criterion (AIC), the mean absolute deviation (MAD), and the measures of intrinsic nonlinearity (INL) and parametric nonlinearity (PNL) were calculated. The nonlinear multivariate model LL was adequate and achieved satisfactory results to describe the productive traits of sunn hemp.

A comprehensive comparison of copula models and multivariate normal distribution for geo-material parametric data

The role of physical oceanographical, geochemical, and sedimentological data in the problem of estimating ocean primary productivity is analyzed using geostatistical and algebraic multivariate spatial methods. The available maps mirror difficulties in measuring productivity directly and quantifying biological observations, which result in a very spotty survey coverage of the world's oceans. This paper takes an approach of estimating the target productivity from related sedimentological, physical oceanographical, and marine geochemical variables. The variables are considered as a multivariate spatial system. Geostatistical estimation is applied to fill in the survey gaps, and the individual data sets are then integrated into a multivariate spatial model using algebraic map comparison. Results are used in the quality assessment and calibration of transform models between the proxy variables and primary productivity. For the Atlantic Ocean, case studies are carried out for phosphate distribution at the 100 m level, foraminifera abundance in sediments, and sea surface temperature. The utility of each proxy variable in the prediction of productivity is discussed. A new map of phosphate concentration at the 100 m level with full coverage of the Atlantic Ocean is compiled by application of geostatistics to an enlarged data base containing new observations. Primary productivity can be predicted from this phosphate map, using transforms that involve also distance from the coastline, and latitude (photosynthesis restriction). Foraminifera abundance is in principle closely related to productivity and is of importance in view of a paleoceanographic reconstruction, but difficulties in measuring and quantifying reflected in the quality of the data set prohibit a direct estimation. The relationship between higher fertility and lower temperature known from upwelling areas does not provide a simple global predictor; instead, sea surface temperature seasonality is an indicator of primary productivity under the constraint of regional availability of nutrients.

Under the context of urban compound air pollution, the joint dependence structure and spatiotemporal characteristics between NO2 and PM2.5 have not yet been systematically quantified. To reveal their co-variation mechanisms, this study utilizes daily average data from 31 air quality monitoring stations covering urban and suburban areas of Beijing during 2023-2024. A staged analytical framework integrating overall modeling, spatial clustering, and seasonal stratification is constructed. First, a mixture copula model is employed to characterize the overall joint distribution of NO2 and PM2.5. Subsequently, statistical fingerprint clustering combined with seasonal analysis is applied to identify spatial and temporal heterogeneity in the dependence structure. The results indicate a moderately strong positive dependence between NO2 and PM2.5 across Beijing, with an asymmetric structure featuring upper-tail-dominant dependence structure. This suggests that the two pollutants are more likely to increase synchronously under high-pollution conditions, implying a joint amplification effect during extreme pollution episodes. Spatial clustering analysis reveals significant gradient differences in concentration levels among monitoring stations, particularly for NO2, which exhibits significant spatial stratification. However, the form of the dependence structure remains relatively stable, indicating that spatial location primarily influences pollution intensity rather than coupling mechanisms. Seasonal variation substantially restructures the joint distribution. During the heating season, the two pollutants exhibit strong positive dependence and lower tail dependence, whereas in the non-heating season, the dependence is characterized by upper-tail-dominant feature. These findings suggest that seasonal factors exert a stronger regulatory effect on the pollutant dependence structure than spatial differences. This study reveals the spatiotemporal characteristics of the synergistic evolution of NO2 and PM2.5 in Beijing, providing support for joint risk assessment of extreme pollution events and seasonally differentiated coordinated control strategies.

SummaryThe integrated nested Laplace approximation (INLA) is a convenient way to obtain approximations to the posterior marginals for parameters in Bayesian hierarchical models when the latent effects can be expressed as a Gaussian Markov random field. In addition, its implementation in the R-INLA package for the R statistical software provides an easy way to fit models using the INLA in practice in a fraction of the time that other computer-intensive methods (e.g. Markov chain Monte Carlo methods) take to fit the same model. Although the INLA provides a fast approximation to the marginals of the model parameters, it is difficult to use it with models that are not implemented in R-INLA. It is also difficult to make multivariate posterior inference on the parameters of the model as the INLA focuses on the posterior marginals and not the joint posterior distribution. We describe how to use the INLA within the Metropolis–Hastings algorithm to fit complex spatial models and to estimate the joint posterior distribution of a small number of parameters. We illustrate the benefits of this new method with two examples. In the first, a spatial econometrics model with two auto-correlation parameters (for the response and the error term) is considered. This model is not currently available in R-INLA, and multivariate inference is often required to assess dependence between the two spatial auto-correlation parameters in the model. Furthermore, the estimation of spillover effects is based on the joint posterior distribution of a spatial auto-correlation parameter and a covariate coefficient. In the second example, a multivariate spatial model for several diseases is proposed for disease mapping. This model includes a shared specific spatial effect as well as disease-specific spatial effects. Dependence on the shared spatial effect is modulated via disease-specific weights. By inspecting the joint posterior distribution of these weights it is possible to assess which diseases have a similar spatial pattern.

Two probabilistic forecasting models for the clear-sky index, based on the Markov-chain mixture distribution (MCM) and copula clear-sky index generators, are presented and evaluated. In terms of performance, these models are compared with two benchmark models: a Quantile Regression (QR) model and the Persistence Ensemble (PeEn). The models are tested on minute resolution clear-sky index data, which was estimated from irradiance data for two different climatic regions: Hawaii, USA and Norrkoping, Sweden. Results show that the copula model generally outperforms the PeEn, while the MCM and QR models are superior in all tested aspects. Comparing MCM and QR reliability, the QR is superior, while the MCM is superior in mean CRPS and skill score. The MCM model is proposed as a potential benchmark for probabilistic solar forecasting. The MCM model is available in Python as SheperoMah/MCM-distribution-forecasting at GitHub.

This research explores the development of a reversionary annuity product transformed into a family annuity covering three individuals: husband, wife, and children. The innovative design of this product considers the sequencing of annuity payments post-participant's demise, aiming to mitigate the risk of parents' death impacting their children. Recognizing the inadequacy of assuming independence among individuals in premium calculations, the study employs a multivariate Archimedean Copula model to account for interdependence. The primary objective is to compute the survival single-life function for each individual taken from TMI IV 2009. Then the copula model is implemented with Clayton and Frank copulas at varying Kendall’s tau values (0.25, 0.5, and 0.75). Meanwhile, the interest rates are modeled using the BI-7-day (reverse) rate with a Triangular Fuzzy α-cut. The findings reveal that increasing Kendall’s tau values lead to higher pure premiums, and notably, the Frank Copula model yields higher premium values than the Clayton Copula model. This research contributes valuable insights into the actuarial assessment of family annuity products, shedding light on the significance of considering dependencies among individuals for more accurate premium calculations.

Multivariate simulation using a locally varying coregionalization model