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Local structure graph models (LSGMs) describe random graphs and networks as a Markov random field (MRF)—each graph edge has a specified conditional distribution dependent on explicit neighbourhoods of other graph edges. Centred parameterizations of LSGMs allow for direct control and interpretation of parameters for large- and small-scale structures (e.g., marginal means vs. dependence). We extend this parameterization to account for triples of dependent edges and illustrate the importance of centred parameterizations for incorporating covariates and interpreting parameters. Using a MRF framework, common exponential random graph models are also shown to induce conditional distributions without centred parameterizations and thereby have undesirable features. This work attempts to advance graph models through conditional model specifications with modern parameterizations, covariates and higher-order dependencies. Les modèles graphiques à structure locale (MGSL) décrivent des graphes aléatoires et des réseaux comme des champs aléatoires markoviens (CAM) -- chaque arête se voyant attribuer une distribution conditionnelle dépendant explicitement du voisinage d’autres arêtes. Les paramétrisations centrées de MGSL permettent un contrôle direct et une interprétation des paramètres des structures, qu’elles soient à petite ou à grande échelle (p.ex. les moyennes marginales vs la dépendance). Les auteurs étendent cette paramétrisation afin qu’elle tienne compte de trios d’arêtes dépendantes et illustrent l’importance des paramétrisations centrées afin d’incorporer des covariables et d’interpréter les paramètres. À partir d’un cadre de CAM, les auteurs montrent que les modèles graphiques aléatoires exponentiels communs induisent des distributions conditionnelles sans paramétrisation centrée, leur conférant ainsi des propriétés indésirables. Ces travaux tentent de faire avancer les modèles graphiques par une approche conditionnelle de spécification avec des paramétrisations modernes, des covariables, et des dépendances d’ordre supérieur.

We present the methods employed by team ‘Uniofbathtopia’ as part of a competition organised for the 13th International Conference on Extreme Value Analysis (EVA2023), including our winning entry for the third sub-challenge. Our approaches unite ideas from extreme value theory, which provides a statistical framework for the estimation of probabilities/return levels associated with rare events, with techniques from unsupervised statistical learning, such as clustering and support identification. The methods are demonstrated on the data provided for the EVA (2023) Conference Data Challenge – environmental data sampled from the fantasy country of ‘Utopia’ – but the underlying assumptions and frameworks should apply in more general settings and applications.

Private businesses in sectors, such as food, energy, and retail, as well as public sector and federal agencies are interested in the predictive understanding of weather impacts on crop yield, which is an important aspect of food security. Scientific literature has mainly examined how crop yield is impacted by growing season-averaged weather indices. Although a few studies did consider weather extremes in their analysis, their scope was either restricted to measuring their conditional relationship with yield or the extreme event types considered were limited. Selection of regression models, whether the more commonly used linear approaches or nonlinear methods, have not been appropriately justified in this context. Here, we develop data-driven methods to examine two inter-related hypotheses for improved scientific understanding and enhanced predictive modeling. The first hypothesis, that extreme weather indices have a statistically significant information content in them is found to be valid based on linear and nonlinear methods for pairwise dependence. The second hypothesis, examines the value addition of nonlinear regression methods, and suggests that linear approaches may not alone be adequate. The results of this study can inform scientific understanding, generation and relevance of indices and end-to-end risk assessment systems in the context of climate impacts on crop yield. An immediate application may be in the context of NASA Earth Exchange (NEX) which facilitates the generation and dissemination of impacts relevant weather data and indices using a multitude of satellite-derived data sets and model outputs.

Extreme opinion propagation in social information networks often appears as a low-frequency but high-impact process, in which abnormal activity becomes synchronized across structurally related users or communities during crisis periods. Conventional correlation-based methods mainly describe average co-movement and may therefore miss dependence patterns that emerge only in the tail regime. To address this issue, this paper proposes a community-structured extremal dependence framework for social opinion propagation risk analysis. A tail pairwise dependence matrix (TPDM) is used to construct a weighted extremal dependence network, on which node-level risk scoring, community detection, and community-level intervention analyses are performed. The proposed risk score integrates degree centrality, betweenness centrality, tail exposure, and community embedding strength, while the intervention component is formulated as a minimum cut problem on the induced community graph. The framework is evaluated on a controlled synthetic social discussion network with 100 nodes. The experiment is intended as a methodological proof of concept rather than as a real-platform empirical validation. The results show that the TPDM-based network produces a structured representation with two dominant coupled communities, several peripheral singleton nodes, concentrated high-risk nodes, and one principal source–target interface in the community graph. These findings indicate that extremal dependence can provide a useful representation of candidate risk-coupling structures under the synthetic setting. However, the inferred edges should not be interpreted as causal propagation paths, and the minimum cut result should be understood as a candidate intervention interface rather than as a guarantee of complete diffusion blockage. Future work should validate the framework on real social media traces, incorporate temporal causal information, and examine robustness under multi-channel diffusion and adaptive user behavior.

Information theory provides robust measures of multivariable interdependence, but classically does little to characterize the multivariable relationships it detects. The Partial Information Decomposition (PID) characterizes the mutual information between variables by decomposing it into unique, redundant, and synergistic components. This has been usefully applied, particularly in neuroscience, but there is currently no generally accepted method for its computation. Independently, the Information Delta framework characterizes non-pairwise dependencies in genetic datasets. This framework has developed an intuitive geometric interpretation for how discrete functions encode information, but lacks some important generalizations. This paper shows that the PID and Delta frameworks are largely equivalent. We equate their key expressions, allowing for results in one framework to apply towards open questions in the other. For example, we find that the approach of Bertschinger et al. is useful for the open Information Delta question of how to deal with linkage disequilibrium. We also show how PID solutions can be mapped onto the space of delta measures. Using Bertschinger et al. as an example solution, we identify a specific plane in delta-space on which this approach’s optimization is constrained, and compute it for all possible three-variable discrete functions of a three-letter alphabet. This yields a clear geometric picture of how a given solution decomposes information.

Local structure graph models (LSGMs) describe random graphs and networks as a Markov random field (MRF)—each graph edge has a specified conditional distribution dependent on explicit neighbourhoods of other graph edges. Centered parameterizations of LSGMs allow for direct control and interpretation of parameters for large- and small-scale structures (e.g., marginal means vs. dependence). Here, we extend this parameterization to account for triples of dependent edges and illustrate the importance of centered parameterizations for incorporating covariates and interpreting parameters. Using a MRF framework, common exponential random graph models are also shown to induce conditional distributions without centered parameterizations and thereby have undesirable features. This work attempts to advance graph models through conditional model specifications with modern parameterizations, covariates and higher-order dependencies.

In this study, we prove a mean convergence theorem for the partial sums from triangular arrays of rowwise and pairwise -negatively dependent random variables, where may be unbounded. The main theorem extends Theorem 3.1 of Chen, Bai, and Sung (J. Math.  Anal. Appl. 419 , 1290–1302 (2014)).

This paper introduces the notion of pairwise and coordinatewise negative dependence for random vectors in Hilbert spaces. Besides giving some classical inequalities, almost sure convergence and complete convergence theorems are established. Some limit theorems are extended to pairwise and coordinatewise negatively dependent random vectors taking values in Hilbert spaces. An illustrative example is also provided.

We propose an algorithm to sample the area of the smallest convex hull containing n sample points uniformly distributed over unit square. To do it, we introduce a new coordinate system for the position of vertexes and re-write joint distribution of the number of vertexes and their locations in the new coordinate system. The proposed algorithm is much faster than existing procedure and has a computational complexity on the order of O ( T ) , where T is the number of vertexes. Using the proposed algorithm, we numerically investigate the asymptotic behavior of functionals of the random convex hull. In addition, we apply it to finding pairs of stocks where the returns are dependent on each other on the New York Stock Exchange.