Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems
In the last years the reputation of medical, economic, and scientific expertise has been strongly damaged by a series of false predictions and contradictory studies. The lax application of statistical principles has certainly contributed to the uncertainty and loss of confidence in the sciences. Var...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/5986562 |
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| author | Michele Lungaroni Andrea Murari Emmanuele Peluso Pasqualino Gaudio Michela Gelfusa |
| author_facet | Michele Lungaroni Andrea Murari Emmanuele Peluso Pasqualino Gaudio Michela Gelfusa |
| author_sort | Michele Lungaroni |
| collection | DOAJ |
| description | In the last years the reputation of medical, economic, and scientific expertise has been strongly damaged by a series of false predictions and contradictory studies. The lax application of statistical principles has certainly contributed to the uncertainty and loss of confidence in the sciences. Various assumptions, generally held as valid in statistical treatments, have proved their limits. In particular, since some time it has emerged quite clearly that even slightly departures from normality and homoscedasticity can affect significantly classic significance tests. Robust statistical methods have been developed, which can provide much more reliable estimates. On the other hand, they do not address an additional problem typical of the natural sciences, whose data are often the output of delicate measurements. The data can therefore not only be sampled from a nonnormal pdf but also be affected by significant levels of Gaussian additive noise of various amplitude. To tackle this additional source of uncertainty, in this paper it is shown how already developed robust statistical tools can be usefully complemented with the Geodesic Distance on Gaussian Manifolds. This metric is conceptually more appropriate and practically more effective, in handling noise of Gaussian distribution, than the traditional Euclidean distance. The results of a series of systematic numerical tests show the advantages of the proposed approach in all the main aspects of statistical inference, from measures of location and scale to size effects and hypothesis testing. Particularly relevant is the reduction even of 35% in Type II errors, proving the important improvement in power obtained by applying the methods proposed in the paper. It is worth emphasizing that the proposed approach provides a general framework, in which also noise of different statistical distributions can be dealt with. |
| format | Article |
| id | doaj-art-ffc8644b8a264af684aa6b7cb4c99830 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-ffc8644b8a264af684aa6b7cb4c998302025-02-03T05:59:07ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/59865625986562Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex SystemsMichele Lungaroni0Andrea Murari1Emmanuele Peluso2Pasqualino Gaudio3Michela Gelfusa4Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, ItalyConsorzio RFX (CNR, ENEA, INFN, Universita’ di Padova, Acciaierie Venete SpA), Corso Stati Uniti 4, 35127 Padova, ItalyDepartment of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, ItalyDepartment of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, ItalyDepartment of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, ItalyIn the last years the reputation of medical, economic, and scientific expertise has been strongly damaged by a series of false predictions and contradictory studies. The lax application of statistical principles has certainly contributed to the uncertainty and loss of confidence in the sciences. Various assumptions, generally held as valid in statistical treatments, have proved their limits. In particular, since some time it has emerged quite clearly that even slightly departures from normality and homoscedasticity can affect significantly classic significance tests. Robust statistical methods have been developed, which can provide much more reliable estimates. On the other hand, they do not address an additional problem typical of the natural sciences, whose data are often the output of delicate measurements. The data can therefore not only be sampled from a nonnormal pdf but also be affected by significant levels of Gaussian additive noise of various amplitude. To tackle this additional source of uncertainty, in this paper it is shown how already developed robust statistical tools can be usefully complemented with the Geodesic Distance on Gaussian Manifolds. This metric is conceptually more appropriate and practically more effective, in handling noise of Gaussian distribution, than the traditional Euclidean distance. The results of a series of systematic numerical tests show the advantages of the proposed approach in all the main aspects of statistical inference, from measures of location and scale to size effects and hypothesis testing. Particularly relevant is the reduction even of 35% in Type II errors, proving the important improvement in power obtained by applying the methods proposed in the paper. It is worth emphasizing that the proposed approach provides a general framework, in which also noise of different statistical distributions can be dealt with.http://dx.doi.org/10.1155/2019/5986562 |
| spellingShingle | Michele Lungaroni Andrea Murari Emmanuele Peluso Pasqualino Gaudio Michela Gelfusa Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems Complexity |
| title | Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems |
| title_full | Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems |
| title_fullStr | Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems |
| title_full_unstemmed | Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems |
| title_short | Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems |
| title_sort | geodesic distance on gaussian manifolds to reduce the statistical errors in the investigation of complex systems |
| url | http://dx.doi.org/10.1155/2019/5986562 |
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