Data evaluation and uncertainty estimates for calculated A+M data

Full text: It is a big challenge to develop methods for estimating uncertainties of calculated atomic and molecular data that do not require huge additional computational effort. The present contribution concerns the Unified Monte Carlo (UMC) approach that is well established in the nuclear data community. UMC employs a Bayesian formalism: p(σ) = C × L(y_E,V_E | σ) × p₀(σ | σ_C,V_C) p₀(σ | σ_C,V_C) ~ exp{-(½)[(σ–σ_C)^T • (V_C)-1 • (σ–σ_C)]} L(y_E,V_E | σ) ~ exp{-(½)[(y–y_E)T • (V_E)^-1 • (y–y_E)]}, y=f(σ) Here p₀ is a prior and p a posterior probability, L is a likelihood function for experimental data, y_E and V_E are measured quantities and their uncertainty matrix while σ_C and V_C are model parameters and their uncertainty matrix; function f implements the model. Metropolis (Markov chain) sampling is used to sample model parameters σ from the probability p and then to obtain the quantities of interest and their estimated uncertainties including correlations. Note that this is very different than fitting a best estimate for the parameter vector σ. We discuss a possible application to the provision of uncertainties and their correlation structure for rovibrational molecular spectroscopy. Two key tools are taken for granted: a method to develop fitted potential energy surfaces (PES), for example, and a method to solve the nuclear Schrödinger equation. The PES is taken as the model prior and then the solution of the nuclear Schrödinger equation together with some accurate measured lines supply the posterior. (author)