Fourier Spectroscopy: A Bayesian Way

Figure 11

(a) Individual posterior sample functions and . (b) 100 posterior sample functions and . The uncertainty at a given frequency is larger for the even function, because for the associated scalings of the two processes holds. (c) 100 spectral samples and 100 offset coefficients mapped to probed data domain. Unlike for the nonoptimised case (see Figure 5(b)), the spread is much smaller, and the quantities connect smoothly at the transition between double- and single-sided regions. (d) 100 samples and measured data . The samples are in agreement with the uncertainty of the measurements. (e) One sample and evaluated inside probed domain ( < 26.36 mm) and outside. With respect to the envelopes , the contributions behave similarly in both domains. (f) 100 samples and evaluated inside the probed domain and outside. Outside the probed domain, the area between the envelops is filled by and . Because the spread in the nonprobed domain is wider than the one in the probed domain, the main uncertainty in the even and odd spectra originates in nonprobed Fourier coefficients.

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