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Center for Nonlinear Studies |
There is a fundamental problem in identifying the peaks in noisy spectra: how many peaks are there in this spectrum? We propose a framework based on Bayesian inference, which enables us to separate multi-peak spectra into the appropriate single peaks statistically. The asymptotic theory of statistical estimation guarantees the peak number estimated by our framework to be correct if the measurement noise is small enough. If otherwise, the estimated peak number become wrong. We show that the changes in the estimated peak number depending on the measurement noise are regarded as phase transitions in statistical estimation, based on the mathematical correspondence between Bayesian inference and statistical physics. We also evaluate the required time interval for measurements to estimate the correct peak number by considering the physical model of spectroscopic measurements.
Host: Michael Chertkov