Fourier Spectroscopy: A Bayesian Way

Figure 12

(a) Means (blue) and (red) obtained for 1000 samples of settings posterior at = 1/2 GHz. Only at the spectral limits the means deviate from the most likely mean (cyan) evaluated at the maximum of the settings posterior. The uncertainty in the zero-path difference causes a considerable deviation from the most likely mean (black). (b) Means (cyan) and (black) after performing numerical marginalisation of settings parameters at = 1/2 GHz. The marginalised means are similar to the means and (see (a)) at the maximum of the settings posterior except for minor differences towards the spectral boundaries. Having the marginalised covariance at hand, 100 samples (blue) and (red) are drawn from the marginalised amplitude posterior. Only in the centre of the spectral domain the spread of increases to capture the uncertainty in as well (see (a)).

(a)

(b)