Joint Multivariate Distribution Research Articles

Diversifying and hedging REIT portfolios with cryptocurrencies: Evidence from global and regional REIT indices

Hedging the financial risk of portfolios of securitized real estate assets is daunting because of the unique nature of the underlying assets and because no direct market exists to trade on property-related derivatives. In this paper, we conduct a global study of the diversification and risk mitigation benefits of cryptocurrencies for REIT stocks. Specifically, we examine the dynamic relationship between Bitcoin and REIT indices obtained from multiple countries and regions of the world. We also explore whether portfolios of REIT stocks that are hedged with Bitcoin futures obtain significant improvement in portfolio risk mitigation and return performance. Furthermore, given that Bitcoin and REIT stocks are prone to large volatility swings, we examine the nature of the tail dependences in the multivariate distributions of our REIT indices universe and Bitcoin using Archimedean copula functions. Lastly, we compare the market risk of Bitcoin-hedged REIT portfolios to the unhedged portfolios of REIT stocks using value-at-risk. We find region-specific benefits from using Bitcoin to hedge REIT exposure. Furthermore, we show that using Bitcoin to dynamically hedged REIT portfolios had minimal impact on the bivariate and multivariate joint distributions of REIT portfolios. We also find evidence of region-specific reductions in the market risk exposure of dynamically hedged REIT portfolios relative to unhedged and naively hedged REIT portfolios. We posit that Bitcoin could improve the mean-variance frontiers of REIT investors in countries with higher market friction and lower global integration.

Regression generative adversarial network based on bounded losses for prediction of free calcium oxide in cement clinker

The data imbalance problem caused by multi-time scales phenomenon affects the prediction accuracy, validity and robustness of free calcium oxide (fCaO) content in cement clinker calcination process. Focusing on this problem, we propose an regression generative adversarial network model to predict fCaO content, which contains a generator, discriminator and predictor. Generator and discriminator are designed as bounded loss generative adversarial network to solve mode collapse problem and improve the stability. They learn actual data features in adversarial learning style and produce fake data to enlarge the scale and feature space of actual data to train predictor and finally achieve the prediction of fCaO content, which overcomes the problem of data imbalance. For performance assessment, we visually evaluate the validity of generated data from the perspective of univariate distribution and multivariate joint distribution and invent sequence change tendency consistency index (TCI) to evaluate the robustness of fCaO content prediction. Experiments implemented by cement production data demonstrate that the proposed model has advantages in accuracy, availability and robustness in fCaO content prediction, especially TCI is higher 22.69 percentage points than that of without data augmentation.

A Framework for Analyzing Individual-Tree and Whole-Stand Growth by Fusing Multilevel Data: Stochastic Differential Equation and Copula Network

In forestry, growth functions form the basis of research and are widely used for the mathematical modeling of stand variables, e.g., tree or stand basal area, stand height, stand volume, site index, and many more. In this study, to estimate five-dimensional dependencies between tree diameter at breast height, potentially available area, height, crown area and crown base height, we used a normal copula approach whereby the growths of individual variables are described using a stochastic differential equation with mixed-effect parameters. The normal copula combines the marginal distributions of tree diameter at breast height, potentially available area, height, crown area, and crown base height into a joint multivariate probability distribution. Copula models have the advantage of being able to use collected longitudinal, multivariate, and discrete data for which the number of measurements of individual variables does not match. This study introduced a normalized multivariate interaction information measure based on differential entropy to assess the causality between tree size variables. In order to accurately and quantitatively assess the stochastic processes of the tree size variables’ growth and to provide a scientific basis for the formalization of models, an analysis method of the synergetic theory of information entropy has been proposed. Theoretical findings are illustrated using an uneven-aged, mixed-species empirical dataset of permanent experimental plots in Lithuania.

A quantity-distribution synthesized framework for risk assessment of algal blooms

Algal blooms threaten water safety and quality, particularly in lakes with vulnerable environment and advanced urbanization. Due to low water exchange rate and multiple human activity influences, algal blooms in inland lakes display highly dynamic spatio-temporal distributions. This paper proposes a comprehensive framework for risk assessment of algal bloom coupling quantity and distribution based on remote sensing observations. The framework comprises algal bloom recognition, spatial zonation, quantity-distribution multivariate joint distribution construction, and risk assessment. The framework was applied to China's giant shallow and algae-prone lake, Chaohu Lake, to assess the annual algal bloom risk from 2000 to 2021. The results showed that this proposed method could achieve a more comprehensive and objective risk assessment by coupling the quantity and distribution of algal blooms. Furthermore, the internal dependence of algal bloom fluctuation in different zones was explicitly presented. This framework promotes systematic integration of algal bloom risk assessment, taking into account its highly spatio-temporal dynamic feature. It creates a quantitative approach to gain insights into the evolution of quantity and distribution in various environmental assessments.

Quantifying and clustering the wake-induced perturbations within a wind farm for load analysis

The main objective of the HIPERWIND project is to reduce the Levelized Cost Of Energy by controlling the uncertainties in a chain of numerical models simulating an offshore wind farm. This paper studies the wake-induced perturbations of the ambient wind conditions inside a wind farm. A theoretical floating offshore wind farm off the coast of South Brittany in France is considered as a test case, and a numerical model simulating the wake of this farm is exploited. This model gives an analytical prediction of wake deficit and added turbulence, also considering the influence of the floaters’ position due to mean wind forces. An uncertainty propagation on the wake model is performed, considering the multivariate joint distribution of ambient wind conditions as input. This results, for each turbine, in a wake-modified probabilistic distribution on the wind speed and turbulence intensity averaged over the rotor. A new approach for clustering these wake-modified distributions is proposed in this paper to regroup the wind turbines exposed to similar environmental conditions, leading to a similar structural response. This analysis is essential to ensure the practical feasibility of the reliability analysis of an overall project with the computational cost of aero-servo-hydro-elastic simulations of offshore wind turbines. Several methods classically used for clustering are compared. Finally, four clusters only are sufficient to represent the whole set of turbines in the wind farm.

Publishing locally private high-dimensional synthetic data efficiently

The existing researches on local differential privacy mainly focus on low-dimensional data. These may be faced with high computation cost or low data accuracy when handling high-dimensional data. LoPub published high-dimensional crowd-sourced data, whose precision decreases with the increase of attributes pairs. In this paper, PrivPJ, a method to preserve local differential privacy of published high-dimensional data, is proposed, which can capture a tradeoff between the availability of results and privacy preservation. In PrivPJ, we design mVAE, a multivariate joint distribution algorithm that can alleviate the effect of increasing attributes pairs on accuracy. Then the complete graph is obtained based on the distribution and Markov network, and a local-differential-private junction tree is built based on the graph. PrivPJ can publish a locally private synthetic dataset with the approximate joint distribution. PrivPJ satisfies local differential privacy, and performs well on computation cost, estimation accuracy and misclassification rate of the algorithm on high-dimensional datasets.

Estimation of outdoor design dataset based on interdependency of multiple meteorological elements by using vine copulas

In building design, the commonly used outdoor weather conditions recommended by ASHRAE are generated by the annual cumulative frequency of occurrence method. This may result in air-conditioning equipment capacity being overestimated. This is because the air temperature, humidity and solar radiation that have the greatest impact on indoor peak cooling loads are selected independently. It means that the probability of these three weather parameters occurring at the same time is extremely small. This paper proposes an approach for selecting the design weather data on the basis of the exact joint distribution with specific simultaneous occurrence probabilities of these three weather parameters. For this purpose, a novel statistical method vine copula is applied to construct the theoretical multivariate joint distributions of these three weather parameters for 24-hour data and combined the design parameters of each hour with a specific simultaneous occurrence probability into a design day. The hourly meteorological records over 10 years in Tokyo are used to generate the outdoor design conditions. The results indicate that the vine copula method can create an effective theoretical model and all the design parameters selected by the simultaneous occurrence probability are significantly below that of the same conventional exceeding probability. For simultaneous occurrence probabilities of 0.4 %, 1 % and 2 %, the corresponding indoor thermal risk levels are 0.46 %, 0.52 % and 0.84 %, respectively. Therefore, the proposed method can be used as a reference for designers to determine a more reasonable capacity of air-conditioning systems.

A systematic framework for the assessment of the reliability of energy supply in Integrated Energy Systems based on a quasi-steady-state model

The reliability analysis of IESs (Integrated Energy Systems) is a complicated task because of the complex characteristics of different subsystems and the multi-scale dynamics that develop therein. To effectively address such problems, this paper proposes a systematic framework to analyse the reliability of energy supply in IESs, considering the dynamics of IESs and the inter-relationships among uncertainties. First, based on the linepack-based performance analysis model of IES, a quasi-steady-state model is established to model the dynamic behaviours in IESs, properly accounting for practical engineering and operational strategies. Then, considering the inter-correlations among different uncertainty sources and time-dependent relationships of each variable, a model that combines the statistical structure of copula with the machine learning method of stacked autoencoder (CSML) is adopted to establish the timely multivariate joint distributions for variables. Monte Carlo simulation combined with Order Statistics is used for assessing supply reliability. Case studies are performed on a realistic IES that combines an IEEE-15 power system with an 18-node natural gas pipeline network. The efficiency and accuracy of the quasi-steady-state model are validated. The reliability evaluation results show that the inter-correlations among variables and time-dependent relationships of each variable have great effects on the system reliability assessment. The consideration of linepack can significantly improve the supply reliability of IES whereas the management strategy of linepack may lead to some risky points.

A multivariate method for evaluating safety from conflict extremes in real time

Several studies have advocated the use of extreme value theory (EVT) traffic conflict models for real-time crash risk prediction using real-time safety indices such as the risk of crash (RC) and return level of a cycle (RLC). This approach provides a logical framework to estimate crash risk by extrapolating from the observed level (i.e., traffic conflict) to the unobserved level (i.e., crash). In these studies, only univariate EVT models that consider only one conflict indicator (e.g. modified time to collision, MTTC) were used which affects the models’ accuracy and precision in estimating crash risk. The use of univariate models is likely due to that existing safety analysis multivariate EVT models have limited capability of delineating the complex dependence structure between multiple conflict indicators for application to real-time safety evaluation. This study proposes a multivariate method for evaluating real-time safety from conflict extremes which consists of novel multivariate EVT models that flexibly integrate multiple conflict indicators and several joint safety indices that comprehensively characterize the safety level of a road facility from multiple dimensions. The proposed approach has several advantages including: 1) it uses four parametric models (tilted Dirichlet, pairwise beta, Husler-Reiss, and extremal-t) for the angular density function for fully describing the dependence level between multiple conflict extremes; and 2) it innovatively develops several important real-time safety indices (e.g., crash risk, joint return levels, and return level concomitant) from the multivariate joint distribution for multidimensionally assessing safety. A seven-step approximate likelihood-based Bayesian inference method for model development is proposed. The proposed model estimation method is applied for cycle-level real-time safety evaluation by combining several conflict indicators at four signalized intersections in the city of Surrey, British Columbia. Three conflict indicators are used: MTTC, post encroachment time (PET), and deceleration rate to avoid a crash (DRAC). Four types of multivariate EVT models were developed. Among these models, for both bivariate and trivariate framework, the Husler-Reiss model has the best goodness-of-fit as it better captures the dependence level among the three conflict indicators. The results indicate that multivariate models identify higher numbers of crash-risk cycles than their corresponding univariate models. Further, most of crash-risk cycles have at least one of joint return levels higher than the threshold (0 for both MTTC and PET, 8.5 m/s2 for DRAC) between a conflict and a collision. For joint return levels from most cycles, one return level exceeds the threshold, while others are lower than the threshold. Under the bivariate framework, all the concomitants of positive return levels are below their own thresholds.

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.

Modeling and optimization for multiple correlated responses with distribution variability

In production design processes, multiple correlated responses with different distributions are often encountered. The existing literature usually assumes that they follow normal distributions for computational convenience, and then analyzes these responses using traditional parametric methods. A few research papers assume that they follow the same type of distribution, such as the t-distribution, and then use a multivariate joint distribution to deal with the correlation. However, these methods give a poor approximation to the actual problem and may lead to the recommended settings that yield substandard products. In this article, we propose a new method for the robust parameter design that can solve the above problems. Specifically, a semiparametric model is used to estimate the margins, and then a joint distribution function is constructed using a multivariate copula function. Finally, the probability that the responses meet the specifications simultaneously is used to obtain the optimal settings. The advantages of the proposed method lie in the consideration of multiple correlation patterns among responses, the absence of restrictions on the response distributions, and the use of nonparametric smoothing to reduce the risk of model misspecification. The results of the case study and the simulation study validate the effectiveness of the proposed method.

A novel approach to form Normal Distribution of Medical Image Segmentation based on multiple doctors' annotations.

Medical image segmentation annotated by experts provides the labeled data sets for many scientific researches. However, due to the unevenly experienced backgrounds of the experts and limited numbers of patients with certain diseases or illnesses, not only do such labeled data sets have smaller samples but their quality and normality also can range in wide variabilities and be ambiguous. In practice, these segmentations are usually assigned to be the ground truths for the scientific studies, so it may undermine the trustworthiness of the resulting findings. Therefore, it is meaningful to consider how to give a more unified opinion of the annotations among different experts. In this paper, a novel approach to form normal distributions of segmentation is proposed based on multiple doctors' annotations for the same patient. The proposed approach is developed through the following steps: (1) utilize a framework7 of averaging images to construct an averaged annotation based on different given annotations; (2) determine the image registration deformations from the averaged annotation to the given annotations; (3) build a joint multivariate Gaussian distribution over the logorithm of Jacobian determinants and curls of the registration deformations; lastly, (4) simulate a normal distribution of segmentation by the joint Gaussian distribution of registration deformation. This work translates the problem of forming a normal distribution of the image segmentation into a problem of forming joint Gaussian distribution of image registration deformations, which the latter can be reasoned by Jacobian determinant (models local size of pixel cells) and curl (models local rotation of pixel cells) information. In the following sections, a detailed walk-through of the proposed approach is provided along with its analytical mathematics and numerical examples for its effectiveness. A synthetic example of 3 manually defined label image is made to show how to construct a mean label image, and an example of a real cancer image annotated by 3 doctors demonstrates the formation of the normal distribution and the effectiveness of the propose method.

Multivariate global agricultural drought frequency analysis using kernel density estimation

Drought frequency analysis provides valuable information for drought risk assessment. Nonparametric kernel density estimation (KDE) is applied for agricultural drought frequency analysis at the global scale. Agricultural drought over 1950–2020 is described by the standardized soil moisture index (SSMI), and drought variables (i.e., duration, severity, and peak) are extracted using run theory. The univariate and multivariate joint distributions of drought variables are established by KDE. Given that the averages for drought duration, severity, and peak are 3.10 (months), 1.59, and 0.60, respectively, the spatial distributions of multivariate return periods are mapped to determine regions with higher drought risk. The results showed that: (1) The mean values of drought duration, severity, and peak over different regions were in the ranges of 1.94–5.18 (months), 0.92–2.81, and 0.49–0.72, respectively. (2) Drought severity had higher correlations with drought duration (0.83) and peak (0.91), while the correlation coefficient between drought duration and peak was lower (0.73). (3) KDE can establish reliable joint distributions of drought variables after passing Kolmogorov-Smirnov (KS) and Anderson-Darling (A-D) tests at the 5% significance level with an average root-mean-square error of 0.04. (4) When the univariate return period was equal to 100 years, the multivariate joint return period of the “or” case was generally less than 70 years but that of the “and” case was mainly greater than 200 years. (5) Compared with other regions, West North America, North-East Brazil, Southeastern South America, Central Asia, and the Tibetan Plateau experienced higher drought risks. Accordingly, countermeasures should be established in these regions to alleviate drought impacts.

Multivariate Dam-Site Flood Frequency Analysis of the Three Gorges Reservoir Considering Future Reservoir Regulation and Precipitation

Under a changing environment, the current hydrological design values derived from historical flood data for the Three Gorges Reservoir (TGR) might be no longer applicable due to the newly-built reservoirs upstream from the TGR and the changes in climatic conditions. In this study, we perform a multivariate dam-site flood frequency analysis for the TGR considering future reservoir regulation and summer precipitation. The Xinanjiang model and Muskingum routing method are used to reconstruct the dam-site flood variables during the operation period of the TGR. Then the distributions of the dam-site flood peak and flood volumes with durations of 3, 7, 15, and 30 days are built by Pearson type III (PIII) distribution with time-varying parameters, which are expressed as functions of both reservoir index and summer precipitation anomaly (SPA). The multivariate joint distribution of the dam-site flood variables is constructed by a 5-D C-vine copula. Finally, by using the criteria of annual average reliability (AAR) associated with the exceedance probabilities of OR, AND and Kendall, we derive the multivariate dam-site design floods for the TGR from the predicted flood distributions during the future operation period of the reservoir. The results indicate that the mean values of all flood variables are positively linked to SPA and negatively linked to RI. In the future, the flood mean values are predicted to present a dramatic decrease due to the regulation of the reservoirs upstream from the TGR. As the result, the design dam-site floods in the future will be smaller than those derived from historical flood distributions. This finding indicates that the TGR would have smaller flood risk in the future.

Study on wind-induced fatigue of heliostat based on artificial neural network

Heliostat is a reflection device in tower solar power station. It is generally arranged in a flat and open area, with an independent column structure. Since the angle needs to be adjusted continuously during use, and the mirror panel suffers a large wind pressure, its support structure is prone to wind-induced fatigue. In this paper, a multivariate joint distribution model was first established based on the law of movement of the heliostat with the sun and the distribution of wind speed and direction. Through a combination of wind tunnel test and finite element analysis, the wind-induced fatigue of typical working conditions was analyzed, and then artificial neural network was used to predict the fatigue life of unknown working conditions. The neural network was improved and tested to make it more consistent with the actual situation, so that it can replace a large amount of work of finite element analysis. Finally, the distribution law of wind-induced fatigue life of heliostats under different factors was summarized, and statistics were performed on the working conditions with high probability fatigue, so as to provide a basis for practical engineering application.

Probabilistic Graphical Models Applied to Spatial Analysis in R: Cell Phone Thefts in Bogotá

Recent technological advances allow large-scale collection, storage and processing information. As a consequence textbf big data has become more important nowadays, since the increase in information has given riseto large and complex data sets that can be potentially exploited to find solutions to relevant problems. Thiswork aims to explain how statistical methods can analyze these large and complex data sets, specifically spatialdata. A spatial dependency analysis is carried out by means of a graph that characterizes the spatial structureand a widely used approach known as Conditional Auto-Regressive (CAR). These models are useful for obtaining multivariate joint distributions of a random vector based on uni-variate conditional specifications. Theseconditional specifications are based on the Markov properties. Hence, that the conditional distribution of acomponent of the random vector depends only on a set of neighbors defined by the graph. CAR models areparticular cases of random Markov fields. Finally, it is explained how to carry out these analyzes in R languageprogramming including the handling of graphs and the packages used. Finally, the parameters estimation inR is carried out following the Bayesian methodology to data corresponding to stolen cell phones in BogotaColombia.

Measuring risk spillovers from multiple developed stock markets to China: A vine-copula-GARCH-MIDAS model

In order to examine the risk spillovers among multiple stock markets efficiently, we develop a vine-copula-GARCH-MIDAS model to estimate the multivariate joint distribution, and then derive CoVaR-type risk measures. Our empirical results on international stock markets show that the vine-copula-GARCH-MIDAS model is promising and is superior to several popular models. One the one hand, it exploits macroeconomic fundamentals to improve the accuracy of CoVaR measure. On the other hand, it is able to measure risk spillovers in a “multiple-to-one” pattern and solve the problem of underestimation in conventional “one-to-one” methods. What’s more, we find that there are significant risk spillovers from multiple developed stock markets including the US, Japan, and Britain, to China, which is necessary for regulators to be concerned with multiple markets simultaneously instead of a single market.

Identifying rainfall threshold of flash flood using entropy decision approach and hydrological model method

Flash flood disaster, with strong suddenness and tremendous destructiveness, is one of the most severe natural disasters in China that seriously threaten the lives and property safety of people and social development. Owing to the complex terrain and limited rainfall and runoff monitoring gauges, it is arduous to effectively prevent and control flash flood disasters in small-sized and medium-sized hilly watersheds. Identifying rainfall threshold, critical discharge and warning periods for flash flood, is critical in disaster prevention in such regions. This study adopted two approaches, the entropy-based decision approach and the hydrological model approach in calculating rainfall thresholds under different antecedent moisture condition (AMC). In particular, the entropy-based decision approach was improved, by using the Frank copula to calculate the multivariate joint distribution of the cumulative rainfall and the corresponding peak discharge. These two approaches were validated in a typical basin, located in the Pearl River Delta in South China that is characterized by frequently heavy rainfall and floods in the monsoon. Results showed that both approaches have the ability to quantify rainfall thresholds. Relatively, the Bayesian method exhibited higher rainfall thresholds, comparing to the other methods. In particular, for AMC I, the utility-entropy risk function method (with λ = 1) exhibited the best-applied practicable forecast lead time of 2.0 h; as for AMC II, the two methods showed the same forecast lead time of 1.5 h, and for AMC III, the hydrological model-based approach showed an optimal forecast lead time of 6.0 h. Meanwhile, the entropy-based approach exhibited the same performance as hydrological modeling approaches, indicating that this method is practicable in flood forecasting. The results would be helpful for floods prevention and mitigation in such small-sized and medium-sized hilly watersheds.

Direct Multivariate Simulation - A stepwise conditional transformation for multivariate geostatistical simulation

Several applications in geoscience require the generation of multiple realizations of random fields of physical properties to mimic their spatial distribution and quantify the model uncertainty. Some modeling problems present complex multivariate distributions with heteroscedasticity and non-linear relations among the variables. We propose a new algorithm, namely Direct Multivariate Simulation, for the simulation of random fields of non-parametric multivariate joint distributions. The methodology is based on a generalization of the normal score and back transformation for multivariate distributions, also called Stepwise Conditional transformation. The sequential sampling of each variable is performed by decomposing the target joint distribution into a product of univariate marginal and conditional probability density functions. We propose numerical solutions to improve the algorithm efficiency for real case applications with a large number of variables. The method is demonstrated through an application where we sample a 6-variate joint distributions with strong nonlinear dependence among the variables. The results are validated by comparing the results to the Projection Pursuit Multivariate Transform and through the computation of the experimental semi-variograms, the marginal distributions, and the bi-histograms of the simulated variables.

A Copula-Based Multivariate Probability Analysis for Flash Flood Risk under the Compound Effect of Soil Moisture and Rainfall

Flash floods can be characterized by several variables. Of these, soil moisture (SM) is an important environmental factor that plays a key role in hydrological and ecological processes and affects the mechanisms that cause flash floods. To more accurately determine the occurrence probability of flash floods, the combined effects of soil moisture and rainfall indexes were considered in this paper, and the copula function approach was explored for use in joint probability analyses of flash flood risks. The results showed that (1) the Clayton copula function offered the best fit for the bivariate joint distribution and captured the occurrence probability of the combination of both peak flow (PF) and SM, while the t-copula function achieved the best fit for the multivariate joint distribution, which presented different combinations of characteristic flash flood parameters. (2) The joint distribution probability of flash floods increased with increasing risk parameter thresholds. Return period analysis indicated that the return periods of the bivariate joint distribution were smaller than those of the multivariate joint distribution. (3) If PF and SM are fixed, the occurrence probability of flash floods is higher in regions where the maximum 1-h rainfall is higher. This study provides an effective and quantitative approach to improving flash flood prediction and advances the application of this approach for the management of future flash flood risks.