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Puy A, Beneventano P, Levin SA, Lo Piano S, Portaluri T, Saltelli A. Models with higher effective dimensions tend to produce more uncertain estimates. SCIENCE ADVANCES 2022. [PMID: 36260678 DOI: 10.5281/zenodo.5658383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Mathematical models are getting increasingly detailed to better predict phenomena or gain more accurate insights into the dynamics of a system of interest, even when there are no validation or training data available. Here, we show through ANOVA and statistical theory that this practice promotes fuzzier estimates because it generally increases the model's effective dimensions, i.e., the number of influential parameters and the weight of high-order interactions. By tracking the evolution of the effective dimensions and the output uncertainty at each model upgrade stage, modelers can better ponder whether the addition of detail truly matches the model's purpose and the quality of the data fed into it.
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Affiliation(s)
- Arnald Puy
- School of Geography, Earth and Environmental Sciences, University of Birmingham, Birmingham B15 2TT, UK
- Department of Ecology and Evolutionary Biology and High Meadows Environmental Institute, Guyot Hall, Princeton University, Princeton, NJ 08544-1003, USA
- Centre for the Study of the Sciences and the Humanities (SVT), University of Bergen, Parkveien 9, PB 7805, 5020 Bergen, Norway
| | - Pierfrancesco Beneventano
- Operations Research and Financial Engineering Department, Princeton University, Princeton, NJ 08544, USA
| | - Simon A Levin
- Department of Ecology and Evolutionary Biology and High Meadows Environmental Institute, Guyot Hall, Princeton University, Princeton, NJ 08544-1003, USA
| | - Samuele Lo Piano
- University of Reading, School of the Built Environment, JJ Thompson Building, Whiteknights Campus, Reading RG6 6AF, UK
| | | | - Andrea Saltelli
- Centre for the Study of the Sciences and the Humanities (SVT), University of Bergen, Parkveien 9, PB 7805, 5020 Bergen, Norway
- Barcelona School of Management, Pompeu Fabra University, Carrer de Balmes 132, 08008 Barcelona, Spain
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Puy A, Beneventano P, Levin SA, Lo Piano S, Portaluri T, Saltelli A. Models with higher effective dimensions tend to produce more uncertain estimates. SCIENCE ADVANCES 2022; 8:eabn9450. [PMID: 36260678 PMCID: PMC9581491 DOI: 10.1126/sciadv.abn9450] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2022] [Accepted: 09/01/2022] [Indexed: 05/20/2023]
Abstract
Mathematical models are getting increasingly detailed to better predict phenomena or gain more accurate insights into the dynamics of a system of interest, even when there are no validation or training data available. Here, we show through ANOVA and statistical theory that this practice promotes fuzzier estimates because it generally increases the model's effective dimensions, i.e., the number of influential parameters and the weight of high-order interactions. By tracking the evolution of the effective dimensions and the output uncertainty at each model upgrade stage, modelers can better ponder whether the addition of detail truly matches the model's purpose and the quality of the data fed into it.
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Affiliation(s)
- Arnald Puy
- School of Geography, Earth and Environmental Sciences, University of Birmingham, Birmingham B15 2TT, UK
- Department of Ecology and Evolutionary Biology and High Meadows Environmental Institute, Guyot Hall, Princeton University, Princeton, NJ 08544-1003, USA
- Centre for the Study of the Sciences and the Humanities (SVT), University of Bergen, Parkveien 9, PB 7805, 5020 Bergen, Norway
- Corresponding author.
| | - Pierfrancesco Beneventano
- Operations Research and Financial Engineering Department, Princeton University, Princeton, NJ 08544, USA
| | - Simon A. Levin
- Department of Ecology and Evolutionary Biology and High Meadows Environmental Institute, Guyot Hall, Princeton University, Princeton, NJ 08544-1003, USA
| | - Samuele Lo Piano
- University of Reading, School of the Built Environment, JJ Thompson Building, Whiteknights Campus, Reading RG6 6AF, UK
| | | | - Andrea Saltelli
- Centre for the Study of the Sciences and the Humanities (SVT), University of Bergen, Parkveien 9, PB 7805, 5020 Bergen, Norway
- Barcelona School of Management, Pompeu Fabra University, Carrer de Balmes 132, 08008 Barcelona, Spain
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Puy A, Sheikholeslami R, Gupta HV, Hall JW, Lankford B, Lo Piano S, Meier J, Pappenberger F, Porporato A, Vico G, Saltelli A. The delusive accuracy of global irrigation water withdrawal estimates. Nat Commun 2022; 13:3183. [PMID: 35676249 PMCID: PMC9177853 DOI: 10.1038/s41467-022-30731-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2021] [Accepted: 05/16/2022] [Indexed: 11/25/2022] Open
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