**Abstract**

Nowadays, an increasing number of scattering measurements rely on the use of large-scale research facilities, which is usually granted after highly competitive peerreviewing and typically for short-time lapses. The optimal use of the allocated time requires rigorous estimates on the reliability of the data analysis, as inferred from the limited statistical accuracy of the measurement. Bayesian inference approaches can significantly help this endeavor by providing investigators with much-needed guidance under challenging decisions on experimental time management. We propose here a method based on the real-time data analysis of running experiments, which fully exploits the core strengths of Bayes theorem. The procedure is implemented in sequential steps in which the spectral measurement is adjourned by summing to it successive acquisition runs, and the spectral modeling is upgraded accordingly. At each stage, the statistical accuracy of the measurement improves, and a more grounded joint posterior distribution is drawn and used as a prior in the subsequent data acquisition stage. The gradual reduction in the model parameters' uncertainty down to the targets set *a priori* by experimenters provides a quantitative "success criterion," which helps prevent oversampling during acquisition. A similar "on the fly" data modeling, might substantially change the way large-scale facilities operate.

**Keywords:** Bayesian inference, neutron and X-ray scattering, spectroscopy, MCMC methods, Bayes theorem, Brillouin neutron scattering
