Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems
Joint Authors
Gaudio, P.
Gelfusa, M.
Andrea, Murari
Lungaroni, Michele
Peluso, Emmanuele
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-08-18
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Lungaroni, Michele& Andrea, Murari& Peluso, Emmanuele& Gaudio, P.& Gelfusa, M.. 2019. Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems. Complexity،Vol. 2019, no. 2019, pp.1-24.
https://search.emarefa.net/detail/BIM-1132300
Modern Language Association (MLA)
Lungaroni, Michele…[et al.]. Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems. Complexity No. 2019 (2019), pp.1-24.
https://search.emarefa.net/detail/BIM-1132300
American Medical Association (AMA)
Lungaroni, Michele& Andrea, Murari& Peluso, Emmanuele& Gaudio, P.& Gelfusa, M.. Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems. Complexity. 2019. Vol. 2019, no. 2019, pp.1-24.
https://search.emarefa.net/detail/BIM-1132300
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1132300