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By Bayesian inference with Metropolis algorithm, we have succeeded highly accurate estimation of a vibrational frequency as well as an initial phase for a damped oscillation contained in coherent phonon signals. Although a rise and damping profile of such vibrating signal impedes high precision estimation in conventional methods based on plane-waves expansion, the Bayesian inference makes it possible to obtain posterior probability distributions of all parameters in an appropriate physical model. On coherent phonon signals with a signal-to-noise ratio of ∼16dB, the probability distribution width of the vibrating frequency becomes two-orders of magnitude smaller than the Fourier spectral width. In addition, we can also estimate the initial phase with an accuracy on the order of 10 milli-radians as well as other parameters

High precision modeling of a damped oscillation in coherent phonon signals by Bayesian inference