Fourier Spectroscopy: A Bayesian Way

Figure 5

Investigation of conditional amplitude posterior for linear parameters . The posterior is obtained for the settings  mm and = 0, = 0 GHz, = 3747.4 GHz, = 5.68 GHz,  V²,  V,  V/m, and  V/m². (a) Spectral posterior means and one posterior sample. Below 1000 GHz, the means show a finite amplitude. Each sample deviates strongly from its corresponding mean. (b) Posterior mean and 100 samples mapped to give even, odd, and offset contributions in data domain. While in the double-sided region () most of the data described by , and give same contributions in the single-sided region (). In the single-sided region, the spread of the even (odd) contributions for the posterior samples is large but bounded by the signal envelops . (c) Residuals for (black) and one sample (red) both mapped to data domain. An almost perfect description of the noisy data is achieved by , indicating an overfitting of the data. (d) Measured data and 100 samples of amplitude posterior mapped to data domain. The individual contributions have a much wider spread (see (b)), but the total sum agrees well with and its uncertainties. This is caused by the posterior covariance of with suited off-diagonal entries.

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