Fourier Spectroscopy: A Bayesian Way

Figure 13

Characterisation of posterior covariance numerically marginalised with respect to settings parameters. is decomposed, so that captures the covariance of the even (odd) spectral quantities. (a) Cross section at frequency = 100.175 GHz. Apart from the extension in the spectral domain, is similar to the covariance evaluated at the maximum of the settings posterior (see Figure 10(a)). shows a significant deviation from (see also (b)). (b) Cross sections of at frequencies = 100.175 GHz, 400.175 GHz, and 850.175 GHz. Towards the spectral limits behaves like . But in the central region a broadband additive contribution is evident originating in the posterior uncertainty of the zero-path difference . (c) Standard deviations evaluated from main diagonal of marginalised covariance (red) and covariance (black, see Figure 10(d)) evaluated at maximum of settings posterior. The odd quantity increases by a factor of three in the central region after the marginalisation. (d) Correlation at three frequencies. Compared to (see Figure 10(c)), a broadband (several 100s GHz) elevation of up to 0.8 follows from the uncertainty in for the central domain.

(a)

(b)

(c)

(d)