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Rank-Based Family of Probability Laws for Testing Homogeneity of Variable Grouping
Publication . Esquível, Manuel L.; Krasii, Nadezhda P.; Nunes, Célia; Opoku-Ameyaw, Kwaku; Mota, Pedro P.; DM - Departamento de Matemática; Faculdade de Ciências e Tecnologia (FCT); CMA - Centro de Matemática e Aplicações; MDPI - Multidisciplinary Digital Publishing Institute
In order to test within-group homogeneity for numerical or ordinal variable groupings, we have introduced a family of discrete probability distributions, related to the Gini mean difference, that we now study in a deeper way. A member of such a family is the law of a statistic that operates on the ranks of the values of the random variables by considering the sums of the inter-subgroups ranks of the variable grouping. Being so, a law of the family depends on several parameters such as the cardinal of the group of variables, the number of subgroups of the grouping of variables, and the cardinals of the subgroups of the grouping. The exact distribution of a law of the family faces computational challenges even for moderate values of the cardinal of the whole set of variables. Motivated by this challenge, we show that an asymptotic result allowing approximate quantile values is not possible based on the hypothesis observed in particular cases. Consequently, we propose two methodologies to deal with finite approximations for large values of the parameters. We address, in some particular cases, the quality of the distributional approximation provided by a possible finite approximation. With the purpose of illustrating the usefulness of the grouping laws, we present an application to an example of within-group homogeneity grouping analysis to a grouping originated from a clustering technique applied to cocoa breeding experiment data. The analysis brings to light the homogeneity of production output variables in one specific type of soil.
Risk-Adjusted Estimation and Graduation of Transition Intensities for Disability and Long-Term Care Insurance
Publication . Curioso, Beatriz A.; Guerreiro, Gracinda R.; Esquível, Manuel L.; DM - Departamento de Matemática; CMA - Centro de Matemática e Aplicações; Faculdade de Ciências e Tecnologia (FCT); MDPI - Multidisciplinary Digital Publishing Institute
This paper introduces a methodology for estimating transition intensities in a multi-state model for disability and long-term care insurance. We propose a novel framework that integrates observable risk factors, such as demographic (age and sex), lifestyle (smoking and exercise habits) and health-related variables (body mass index), into the estimation and graduation of transition intensities, using a parametric approach based on the Gompertz–Makeham law and generalised linear models. The model features four states—autonomous, dead, and two intermediate states representing varying disability levels—providing a detailed view of disability/lack of autonomy progression. To illustrate the proposed framework, we simulate a dataset with individual risk profiles and model trajectories, mirroring Portugal’s demographic composition. This allows us to derive a functional form (as a function of age) for the transition intensities, stratified by relevant risk factors, thus enabling precise risk differentiation. The results offer a robust basis for developing tailored pricing structures in the Portuguese market, with broader applications in actuarial science and insurance. By combining granular disability modelling with risk factor integration, our approach enhances accuracy in pricing structure and risk assessment.
Insuperable Strategies in Two-Player and Reducible Multi-Player Games
Publication . Chalub, Fabio A.C.C.; Souza, Max O.; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; Springer Science + Business Media
Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population from its expected Nash equilibrium. We introduce the concept of insuperable strategy, a strategy that guarantees that no other player can have a larger payoff than the player that adopts it. We show that this concept is different from the rationality assumption frequently used in game theory and that for small populations the insuperable strategy is the most probable evolutionary outcome for any dynamics that equal game payoff and reproductive fitness. We support our ideas with several examples and numerical simulations. We finally discuss how to extend the concept to multiplayer games, introducing, in a limited way, the concept of game reduction.
Fishing effort and enforcement in the Azores Marine Protected Areas
Publication . Moura, Ricardo; Santos, Nuno Pessanha; Catarino, Maria Eduarda; CMA - Centro de Matemática e Aplicações; KeAi Communications Co.
Fishing is a significant global food source, providing protein for millions of people. The Food and Agriculture Organization (FAO) is committed to ensuring access to high-quality food, reducing hunger, and promoting sustainable fisheries to address global population growth and hunger. However, illegal, unreported, and unregulated fishing poses a significant challenge, threatening marine biodiversity and food security. Portugal has the 10th largest Exclusive Economic Zone (EEZ), with waters around mainland Portugal, the Azores, and Madeira. This research focuses on the Azores region, known for its traditional multispecific fishery around the island slopes and seamounts. The region's fisheries face data scarcity issues and complicating effective management. By combining Vessel Monitoring System (VMS) records from 2016 to 2022 and Portuguese Navy (PoN) Fiscalization Reports (FISCREP) from 2015 to 2022, it was possible to use appropriate metrics to characterize the fishing effort and analyze the effectiveness of the inspections conducted in the Azores EEZ. The Total Boat-Meter (TBM) metric combines the number and length of boats to quantify the fishing effort better. The analysis shows that the fishing effort in the protected areas is very high, highlighting the pressure on the protected ecosystems. The findings aim to assist regulatory institutions and researchers in assessing fishing pressure and promoting sustainable fisheries management in the Azores to preserve marine ecosystems.
Updating TCGA glioma classification through integration of molecular data following the latest WHO guidelines
Publication . de Mendonça, Mónica Leiria; Coletti, Roberta; Gonçalves, Céline S.; Martins, Eduarda P.; Costa, Bruno M.; Vinga, Susana; Lopes, Marta B.; CMA - Centro de Matemática e Aplicações; Faculdade de Ciências e Tecnologia (FCT); UNIDEMI - Unidade de Investigação e Desenvolvimento em Engenharia Mecânica e Industrial; DM - Departamento de Matemática; Nature Research
The understanding of glioma disease has significantly advanced through the application of genetic and molecular profiling techniques on brain tumour tissue. Molecular biomarkers have gained a crucial role in glioma diagnosis, driving groundbreaking changes in the disease classification as standardised by the 2016 and 2021 World Health Organisation (WHO) Classification of Tumours of the Central Nervous System. Recent insights from large-scale multi-omics databases, such as The Cancer Genome Atlas (TCGA), have enriched our comprehension of this cancer type. However, given the evolution of glioma classification, retrospective databases may contain outdated annotations, suboptimal for research. To address this issue, we propose two methods for updating the tumor classification of TCGA glioma samples according to the 2016 and 2021 WHO guidelines, through the integration of open-access curated molecular profiling data. Respectively, our Method-2016 and Method-2021 allowed for the diagnostic update of 98% and 87% of cases. The proposed reclassification pipelines, provided in R scripts, enable straightforward reproduction or customisation upon new WHO guideline releases.
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Entidade financiadora
Fundação para a Ciência e a Tecnologia
Programa de financiamento
Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Programático
Número da atribuição
UIDP/00297/2020