Estimation of Circular Statistics in the Presence of Measurement Bias

Circular statistics and Rayleigh tests are important tools for analyzing cyclic events. However, current methods are not robust to significant measurement bias, especially incomplete or otherwise non-uniform sampling. One example is studying 24-cyclicity but having data not recorded uniformly over t...

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Bibliographic Details
Published in:IEEE journal of biomedical and health informatics Vol. 28; no. 2; pp. 1089 - 1100
Main Authors: Alsammani, Abdallah, Stacey, William C., Gliske, Stephen V.
Format: Journal Article
Language:English
Published: United States IEEE 01.02.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Bias
Bioinformatics
Biomarkers
Biomedical measurement
Computer Simulation
Epilepsy
Error correction
Estimation
Fredholm equations
Histograms
Humans
Inference algorithm
Integral equations
inverse problems
nonuniform sampling
parameter estimation
Physics
Probability
Robustness (mathematics)
Sampling
Sleep
Statistical analysis
Statistical significance
Statistical tests
Statistics
Vigilance
ISSN:2168-2194, 2168-2208, 2168-2208
Online Access:Get full text
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Summary:Circular statistics and Rayleigh tests are important tools for analyzing cyclic events. However, current methods are not robust to significant measurement bias, especially incomplete or otherwise non-uniform sampling. One example is studying 24-cyclicity but having data not recorded uniformly over the full 24-hour cycle. Our objective is to present a robust method to estimate circular statistics and their statistical significance in the presence of incomplete or otherwise non-uniform sampling. Our method is to solve the underlying Fredholm Integral Equation for the more general problem, estimating probability distributions in the context of imperfect measurements, with our circular statistics in the presence of incomplete/non-uniform sampling being one special case. The method is based on linear parameterizations of the underlying distributions. We simulated the estimation error of our approach for several toy examples as well as for a real-world example: analyzing the 24-hour cyclicity of an electrographic biomarker of epileptic tissue controlled for states of vigilance. We also evaluated the accuracy of the Rayleigh test statistic versus the direct simulation of statistical significance. Our method shows a very low estimation error. In the real-world example, the corrected moments had a root mean square error of <inline-formula><tex-math notation="LaTeX">\bm {< 0.007}</tex-math></inline-formula>. In contrast, the Rayleigh test statistic overestimated the statistical significance and was thus not reliable. The presented methods thus provide a robust solution to computing circular moments even with incomplete or otherwise non-uniform sampling. Since Rayleigh test statistics cannot be used in this circumstance, direct estimation of significance is the preferable option for estimating statistical significance.
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ISSN:2168-2194
2168-2208
2168-2208
DOI:10.1109/JBHI.2023.3334684