1. Biases in the Simulation and Analysis of Fractal Processes
- Author
-
Didier Delignières, Clément Roume, Samar Ezzina, Hubert Blain, Euromov (EuroMov), Université de Montpellier (UM), and Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)
- Subjects
Article Subject ,0206 medical engineering ,02 engineering and technology ,lcsh:Computer applications to medicine. Medical informatics ,050105 experimental psychology ,General Biochemistry, Genetics and Molecular Biology ,Cross-validation ,Fractal ,Bias ,[SDV.MHEP.PHY]Life Sciences [q-bio]/Human health and pathology/Tissues and Organs [q-bio.TO] ,Humans ,Computer Simulation ,0501 psychology and cognitive sciences ,Statistical physics ,[MATH]Mathematics [math] ,Mathematics ,General Immunology and Microbiology ,Series (mathematics) ,Applied Mathematics ,Rehabilitation ,05 social sciences ,Computational Biology ,Spectral density ,Contrast (statistics) ,General Medicine ,White noise ,Models, Theoretical ,020601 biomedical engineering ,Fractals ,Modeling and Simulation ,Detrended fluctuation analysis ,lcsh:R858-859.7 ,Algorithms ,Autoregressive fractionally integrated moving average ,Research Article - Abstract
Fractal processes have recently received a growing interest, especially in the domain of rehabilitation. More precisely, the evolution of fractality with aging and disease, suggesting a loss of complexity, has inspired a number of studies that tried, for example, to entrain patients with fractal rhythms. This kind of study requires relevant methods for generating fractal signals and for assessing the fractality of the series produced by participants. In the present work, we engaged a cross validation of three methods of generation and three methods of analysis. We generated exact fractal series with the Davies–Harte (DH) algorithm, the spectral synthesis method (SSM), and the ARFIMA simulation method. The series were analyzed by detrended fluctuation analysis (DFA), power spectral density (PSD) method, and ARFIMA modeling. Results show that some methods of generation present systematic biases: DH presented a strong bias toward white noise in fBm series close to the 1/f boundary and SSM produced series with a larger variability around the expected exponent, as compared with other methods. In contrast, ARFIMA simulations provided quite accurate series, without major bias. Concerning the methods of analysis, DFA tended to systematically underestimate fBm series. In contrast, PSD yielded overestimates for fBm series. With DFA, the variability of estimates tended to increase for fGn series as they approached the 1/f boundary and reached unacceptable levels for fBm series. The highest levels of variability were produced by PSD. Finally, ARFIMA methods generated the best series and provided the most accurate and less variable estimates.
- Published
- 2019
- Full Text
- View/download PDF