Project description
Beyond Euclidean limits: building tropical statistical foundations
Traditional statistical methods often prove inadequate for data that resides in non-Euclidean environments, such as the complex geometric structures found in global economics and phylogenetics. Supported by the Marie Skłodowska-Curie Actions programme, the Tropical Statistics project aims to establish a rigorous statistical framework for tropical linear spaces –complex mathematical structures that better represent such data. The project will develop new methods to measure variation and create advanced mathematical models to analyse these unique environments. Key objectives include refining data analysis for faster interpretation and creating an accessible software package in R to help researchers apply these findings. By bridging this gap, Tropical Statistics will provide essential tools for phylogenetics and extreme value theory, enabling scientists to gain deeper insights where classical methods fail.
Objective
Classical statistics assumes data lies in a Euclidean space, but many problems involve non-Euclidean spaces such as manifolds or polyhedral complexes. Tropical linear spaces, which are polyhedral complexes defined by max-linear equations, are a promising but underdeveloped frontier for statistics. Such spaces capture data from a variety of domains, including phylogenetics, extreme-value theory and global economics, where classical methods fail. This proposal develops fundamental statistical measures such as variation, distributions, and models in the tropical setting.
The goal of this proposal is to advance our understanding of statistics in the tropical setting through the following four objectives. (O1) concerns the analysis of variation over tropical linear spaces using tropical principal components under the asymmetric tropical distance. Combining two previous approaches, asymmetric tropical PCA has the potential to offer fast, interpretable analysis of variation of max-linear data. (O2) outlines the next steps for fitting Gauss-Laplace distributions over tropical linear spaces, which is an important step in establishing the foundations of tropical statistics. (O3) defines a tropical probabilistic PCA model, which opens new avenues for statistical testing and Bayesian inference for max-linear data. (O4) implements these advancements in a software package in R, in order to facilitate the use of the results in applications.
Together, these advances lay the foundations for a rigorous statistical framework for tropical linear spaces. This will provide new insights and practical tools for researchers across phylogenetics, extreme-value theory, and global economics.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences computer and information sciences data science
- natural sciences computer and information sciences software
- natural sciences mathematics applied mathematics statistics and probability bayesian statistics
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2025-PF
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
08002 Barcelona
Spain
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.