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Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack polynomials.

This book provides a solution to the ecological inference problem, which has plagued users of statistical methods for over seventy-five years: How can researchers reliably infer individual-level behavior from aggregate (ecological) data? In political science, this question arises when individual-level surveys are unavailable (for instance, local or comparative electoral politics), unreliable (racial politics), insufficient (political geography), or infeasible (political history). This ecological inference problem also confronts researchers in numerous areas of major significance in public policy, and other academic disciplines, ranging from epidemiology and marketing to sociology and quantitative history. Although many have attempted to make such cross-level inferences, scholars agree that all existing methods yield very inaccurate conclusions about the world. In this volume, Gary King lays out a unique--and reliable--solution to this venerable problem. King begins with a qualitative overview, readable even by those without a statistical background. He then unifies the apparently diverse findings in the methodological literature, so that only one aggregation problem remains to be solved. He then presents his solution, as well as empirical evaluations of the solution that include over 16,000 comparisons of his estimates from real aggregate data to the known individual-level answer. The method works in practice. King's solution to the ecological inference problem will enable empirical researchers to investigate substantive questions that have heretofore proved unanswerable, and move forward fields of inquiry in which progress has been stifled by this problem.

This is a review devoted to the complementarity–contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. Bohr contextuality is the dependence of an observable’s outcome on the experimental context; on the system–apparatus interaction. Probabilistically, complementarity means that the joint probability distribution (JPD) does not exist. Instead of the JPD, one has to operate with contextual probabilities. The Bell inequalities are interpreted as the statistical tests of contextuality, and hence, incompatibility. For context-dependent probabilities, these inequalities may be violated. I stress that contextuality tested by the Bell inequalities is the so-called joint measurement contextuality (JMC), the special case of Bohr’s contextuality. Then, I examine the role of signaling (marginal inconsistency). In QM, signaling can be considered as an experimental artifact. However, often, experimental data have signaling patterns. I discuss possible sources of signaling—for example, dependence of the state preparation on measurement settings. In principle, one can extract the measure of “pure contextuality” from data shadowed by signaling. This theory is known as contextuality by default (CbD). It leads to inequalities with an additional term quantifying signaling: Bell–Dzhafarov–Kujala inequalities.

Accurate and reliable assessment of wind energy potential has important implication to the wind energy industry. Most previous studies on wind energy assessment focused solely on wind speed, whereas the dependence of wind energy on wind direction was much less considered and documented. In this paper, a copula‐based method is proposed to better characterize the direction‐related wind energy potential at six typical sites in Hong Kong. The joint probability density function (JPDF) of wind speed and wind direction is constructed by a series of copula models. It shows that Frank copula has the best performance to fit the JPDF at hilltop and offshore sites while Gumbel copula outperforms other models at urban sites. The derived JPDFs are applied to estimate the direction‐related wind power density at the considered sites. The obtained maximum direction‐related wind energy density varies from 41.3 W/m2 at an urban site to 507.9 W/m2 at a hilltop site. These outcomes are expected to facilitate accurate micro‐site selection of wind turbines, thereby improving the economic benefits of wind farms in Hong Kong. Meanwhile, the developed copula‐based method provides useful references for further investigations regarding direction‐related wind energy assessments at various terrain regions. Notably, the proposed copula‐based method can also be applied to characterize the direction‐related wind energy potential somewhere other than Hong Kong.

Lee, U.-J.; Cho, H.-Y.; Lee, B.W., and Ko, D.-H., 2023. Joint probability distribution of significant wave height and peak wave period using Gaussian copula method. In: Lee, J.L.; Lee, H.; Min, B.I.; Chang, J.-I.; Cho, G.T.; Yoon, J.S., and Lee, J. (eds.), Multidisciplinary Approaches to Coastal and Marine Management. Journal of Coastal Research, Special Issue No. 116, pp. 96-100. Charlotte (North Carolina), ISSN 0749-0208. In this study, the joint probability distribution was estimated using the significant wave height-peak wave period data observed for 3 years for 3 stations along the coast of Korea, and an environmental contour line drawing was performed. For accurate estimation, an optimal probability distribution model was calculated for each wave parameter, and the Kolmogorov-Smirnov test and Kullback-Leibler divergence were used for the distribution fit test. Using each estimated optimal probability distribution, a Gaussian copula function was applied considering the correlation between the two wave parameters. As a result of the analysis, it was found that the significant wave height was suitable for the ‘Log-normal’ and ‘3-P Weibull’ distributions, and the peak wave period was suitable for the ‘Log-normal’ distribution. Then, as a result of correlation analysis between significant wave height and peak wave period at all points, it was confirmed that there was a significant correlation. As a result of performing environmental contour line drawing through this, observation data exceeding 3-year recall were found to be less than 1.0% of the total data. In addition, the environmental contour line calculated through the Gaussian Copula showed a limit to reproduce the area where no wave exists as a concave tendency appeared.

The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications. After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications. Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.

Multiple disasters such as strong wind and torrential rain pose great threats to civil infrastructures. However, most existing studies ignored the dependence structure between them, as well as the effect of wind direction. From the dimension of the engineering sector, this paper introduces the vine copula to model the joint probability distribution (JPD) of wind speed, wind direction and rain intensity based on the field data in Yangjiang, China during 1971–2020. First, the profiles of wind and rain in the studied area are statistically analyzed, and the original rainfall amounts are converted into short-term rain intensity. Then, the marginal distributions of individual variables and their pairwise dependence structures are built, followed by the development of the trivariate joint distribution model. The results show that the constructed vine copula-based model can well characterize the dependence structure between wind speed, wind direction and rain intensity. Meanwhile, the JPD characteristics of wind speed and rain intensity show significant variations depending on wind direction, thus the effect of wind direction cannot be neglected. The proposed JPD model will be conducive for reasonable and precise performance assessment of structures subjected to multiple hazards of wind and rain actions.

The accurate probabilistic forecasting of ultra-short-term power generation from distributed photovoltaic (DPV) systems is of great significance for optimizing electricity markets and managing energy on the user side. Existing methods regarding cluster information sharing tend to easily trigger issues of data privacy leakage during information sharing, or they suffer from insufficient information sharing while protecting data privacy, leading to suboptimal forecasting performance. To address these issues, this paper proposes a privacy-preserving deep federated learning method for the probabilistic forecasting of ultra-short-term power generation from DPV systems. Firstly, a collaborative feature federated learning framework is established. For the central server, information sharing among clients is realized through the interaction of global models and features while avoiding the direct interaction of raw data to ensure the security of client data privacy. For local clients, a Transformer autoencoder is used as the forecasting model to extract local temporal features, which are combined with global features to form spatiotemporal correlation features, thereby deeply exploring the spatiotemporal correlations between different power stations and improving the accuracy of forecasting. Subsequently, a joint probability distribution model of forecasting values and errors is constructed, and the distribution patterns of errors are finely studied based on the dependencies between data to enhance the accuracy of probabilistic forecasting. Finally, the effectiveness of the proposed method was validated through real datasets.

This study introduces methodologies for constructing joint probability distribution functions utilizing the Copula function and neural networks, and evaluates their efficacy in marine and civil engineering projects. Through an analytical comparison of both models using a numerical example, it is revealed that the neural network model exhibits superior adaptability to large sample sizes. This adaptability is attributed to the neural network's ability to learn complex relationships within the data, which is especially beneficial when dealing with large datasets. The neural network model also demonstrates higher accuracy in constructing joint probability distribution functions compared to the Copula function model. In marine and civil engineering, the adaptability and accuracy of neural networks are of paramount importance due to the variable and complex nature of weather patterns. A practical engineering application is presented, wherein a joint probabilistic distribution neural network model of wind velocity and rain intensity is established for the Lanzhou–Xinjiang high-speed railroad in China. This model illustrates the promising application of neural networks in engineering projects where weather factors play a critical role. Subsequent to the construction of the joint probability distribution functions, a feature importance analysis is incorporated to quantify the contribution of different weather parameters such as wind velocity and rain intensity to the joint distribution function. This analysis provides an objective assessment of the relative importance of various weather factors and offers data-driven insights that are essential for engineering applications where weather conditions are a significant consideration. The study concludes by highlighting the potential benefits of neural network models in marine and civil engineering, suggesting areas for future exploration.