An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete Information
Motivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the authors and collaborators during the last decade within the framework of the so-called Information Geometric Appr...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/2048521 |
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| author | Sean Alan Ali Carlo Cafaro Steven Gassner Adom Giffin |
| author_facet | Sean Alan Ali Carlo Cafaro Steven Gassner Adom Giffin |
| author_sort | Sean Alan Ali |
| collection | DOAJ |
| description | Motivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the authors and collaborators during the last decade within the framework of the so-called Information Geometric Approach to Chaos (IGAC). The IGAC is a theoretical modeling scheme that combines methods of information geometry with inductive inference techniques to furnish probabilistic descriptions of complex systems in presence of limited information. In addition to relying on curvature and Jacobi field computations, a suitable indicator of complexity within the IGAC framework is given by the so-called information geometric entropy (IGE). The IGE is an information geometric measure of complexity of geodesic paths on curved statistical manifolds underlying the entropic dynamics of systems specified in terms of probability distributions. In this manuscript, we discuss several illustrative examples wherein our modeling scheme is employed to infer macroscopic predictions when only partial knowledge of the microscopic nature of a given system is available. Finally, we include comments on the strengths and weaknesses of the current version of our proposed theoretical scheme in our concluding remarks. |
| format | Article |
| id | doaj-art-0cc92ef71a1e4cf9aeac255bee275064 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-0cc92ef71a1e4cf9aeac255bee2750642025-02-03T01:25:42ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/20485212048521An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete InformationSean Alan Ali0Carlo Cafaro1Steven Gassner2Adom Giffin3Albany College of Pharmacy and Health Sciences, 12208 Albany, NY, USASUNY Polytechnic Institute, 12203 Albany, NY, USASUNY Polytechnic Institute, 12203 Albany, NY, USAClarkson University, 13699 Potsdam, NY, USAMotivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the authors and collaborators during the last decade within the framework of the so-called Information Geometric Approach to Chaos (IGAC). The IGAC is a theoretical modeling scheme that combines methods of information geometry with inductive inference techniques to furnish probabilistic descriptions of complex systems in presence of limited information. In addition to relying on curvature and Jacobi field computations, a suitable indicator of complexity within the IGAC framework is given by the so-called information geometric entropy (IGE). The IGE is an information geometric measure of complexity of geodesic paths on curved statistical manifolds underlying the entropic dynamics of systems specified in terms of probability distributions. In this manuscript, we discuss several illustrative examples wherein our modeling scheme is employed to infer macroscopic predictions when only partial knowledge of the microscopic nature of a given system is available. Finally, we include comments on the strengths and weaknesses of the current version of our proposed theoretical scheme in our concluding remarks.http://dx.doi.org/10.1155/2018/2048521 |
| spellingShingle | Sean Alan Ali Carlo Cafaro Steven Gassner Adom Giffin An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete Information Advances in Mathematical Physics |
| title | An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete Information |
| title_full | An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete Information |
| title_fullStr | An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete Information |
| title_full_unstemmed | An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete Information |
| title_short | An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete Information |
| title_sort | information geometric perspective on the complexity of macroscopic predictions arising from incomplete information |
| url | http://dx.doi.org/10.1155/2018/2048521 |
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