For the design and modelling of reactive flows, profound knowledge of temperature and species concentration is essential. Here, optical, non-invasive sensing techniques are frequently chosen, yet they often require elaborate experimental effort or inhibit other disadvantages. To circumvent these drawbacks, we developed a mobile, fiber-based sensor system, utilizing linear rotational Raman spectroscopy. This technique requires neither sampling from or tracers inside the reactive flow nor an external temperature or composition calibration. It simultaneously yields point-wise information on temperature and species concentration. To extract these quantities of interest the acquired, background-corrected spectra are matched to simulated spectra via a least-square fit algorithm. Such an approach constitutes an ill-posed inverse problem as multiple solutions could explain the measured data. Conventional least-square approaches only yield a set of parameters minimizing the residuum, but neglect uncertainties arising from the ill-posedness. Here, Bayesian inference offers many advantages: besides pointestimates it allows to determine the corresponding uncertainties. Furthermore, prior knowledge about quantities of interest or model parameters can be included in the evaluation to establish a more advanced analysis routine. Using these tools, the benefits and limits of the rotational Raman technique are evaluated by the investigation of a flame from a premixed methane/air laminar flat-flame burner regarding the flame temperature and species concentrations of the rotational Raman-active and, therefore, detectable gas species N2, O2 and CO2. In addition, two different backgroundcorrection approaches are applied and compared using Bayesian inference and inter-parameter correlations.