Fourier Spectroscopy: A Bayesian Way

Figure 10

Characterisation of posterior covariance for amplitude parameters obtained at maximum of settings posterior for = 1/2 GHz (see Table 1). (a) Cross section of covariances and for even and odd function. Each covariance is similar to a sinc function centred at , where a tip is added on top. (b) Cross section of covariances and . At a fixed frequency, and are independent, because = 0. But finite correlation remains with the neighbouring spectral domain. (c) Correlation. The even (odd) parameters are correlated () over the spectral scale of about 1.5 GHz (10 GHz), while the correlation between even and odd parameters is small and asymmetric with respect to . (d) Standard deviations and . At the spectral limits the uncertainties approach zero. (e) and (f) Correlations of and . The correlations are oscillating and decrease generally with the frequency.

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