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Signals as departures from random walks
Glenn Ierley1, Alex Kostinski2
1Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, Michigan 49931, USA and Scripps Institution of Oceanography, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0225, USA.
Physical Review. E
|July 20, 2022
Summary
This study introduces a novel method using random walks to detect signals in data by analyzing sampling variability. It helps identify deviations from independent and identically distributed (IID) noise, aiding signal extraction.
Area of Science:
- Statistics
- Signal Processing
- Data Analysis
Background:
- Understanding data variability is crucial for signal detection.
- Independent and identically distributed (IID) processes are common in data analysis.
- Existing methods for signal extraction can be complex and noise-dependent.
Purpose of the Study:
- To develop a method for distinguishing true signals from random noise in data.
- To provide confidence bounds for assessing data variability.
- To offer a signal extraction technique easily combinable with other methods.
Main Methods:
- Utilizing a distribution-invariant discrete eigenvalue spectrum for IID processes.
- Employing a cumulative distribution function in rank and time to map sampling variability to random walks.
- Analyzing residuals (data with signal removed) for deviations from expected IID variability.
Main Results:
- The random walk mapping provides confidence bounds for signal detection.
- Deviations from IID sampling variability are identified as significant signals.
- The method is effective in analyzing datasets with dark current and gamma-ray arrivals.
Conclusions:
- The proposed method offers a robust way to detect signals in various data types.
- This approach simplifies signal extraction by focusing on deviations from IID noise.
- The technique is versatile and can be integrated with existing signal processing tools.
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