Bayesian sampling recovers physical parameters and their uncertainties
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Inferring physical conditions from observations is often an inverse problem: a nonlinear numerical model predicts the data from physical parameters, and the observations must then be used to work backwards. In astrophysics this problem is particularly demanding because model predictions can span many orders of magnitude, measurements contain several kinds of noise, weak signals are censored by detection limits, and different physical solutions may explain the same observations.
We developed a Bayesian sampler designed for this combination of difficulties. It couples a local exploration method, which efficiently samples each probability mode, with a multiple-try step that allows the algorithm to jump between distinct modes. Applied to a realistic synthetic molecular-cloud problem based on a photodissociation-region model, the method reconstructs maps of thermal pressure, UV radiation field, and visual extinction while also providing spatially resolved credibility intervals.
The uncertainty maps are as important as the parameter estimates themselves: they identify where the observations contain enough information to constrain a physical quantity and where degeneracies or sensitivity limits remain. This provides a statistically controlled route from complex molecular-line data to physical maps in situations where the true answer is not available for comparison.
Figure: Synthetic benchmark for Bayesian inference of molecular-cloud physical conditions. The four rows show the parameters \(\kappa\), \(P_\mathrm{th}\), \(G_0\), and \(A_V\). For each parameter, the synthetic truth is compared with a usual pixel-wise maximum-likelihood estimate and with the new MMSE reconstruction including spatial regularization; the rightmost column gives the corresponding 95% credibility intervals. The bottom panels show examples of the synthetic observations used for the inversion: excited CO line maps generated with Meudon PDR models and noise, together with the fraction of undetected lines. The comparison illustrates how spatial regularization improves the recovery of coherent physical structures while retaining spatially resolved uncertainty estimates.