Sprecher
Beschreibung
In adaptive Bayesian spectroscopy, physics fixes the forward model and what remains is the choice of prior. This prior also implicitly encodes a certain effective size of the model which make model and prior selection overlapping problems. In spectroscopy we typically have real structural knowledge. Qualitatively speaking, spectra are smooth, variance is finite, certain frequency ranges matter. But this constrains hyperparameters only to plausible regions, not to specific values. Marginalizing over a diffuse hyperprior gives support to unphysical regions, while a sharp one encodes precision we lack. In practice we compare a finite candidate set via Bayesian evidence, but correlated candidates (e.g., smoothness priors at neighboring length scales) let densely sampled regions of model space accumulate disproportionate weight, making results sensitive to an arbitrary discretization. We present these tensions from information-optimal Fourier-transform spectroscopy and invite discussion on navigating the space between "I know something" and "I can write down a measure."