We propose a systematic Bayesian method for inferring the mineral composition of rock samples from transmission Fourier‐transform infrared spectroscopy (FTIR) measurements. Currently available FTIR inversion methodologies depend on measuring pure minerals, using them within least‐squares approaches with a hand‐tuned noise model, and implementing ad hoc post‐processing of the obtained solution. Within the proposed data‐driven framework, we replaced these previous inversion approaches with the automatic training and estimation steps. In this approach, the linear operator, comparable with the FTIR spectral standards (FTIR spectra of end‐members or pure minerals), is estimated or trained on a calibration set of rock samples for which the mineral composition has been accurately determined by other means in the laboratory. With this linear operator, we then quantify the spectral‐noise covariance matrix from the calibration set, which forms the basis of our estimation of the Bayesian posterior uncertainty on a mineral‐composition estimate. This quantification of uncertainty in mineral estimation is a novel feature that can be used as a reliability measure. The uncertainty also describes the correlation between estimates of mineral‐weight fractions, indicating which pairs of minerals cannot be independently estimated. Our Bayesian model also addresses the uncertainty propagated from the estimated linear operator and thus captures a possible mismatch of the model parameter from the true operator (i.e., semiblindness of the model). We demonstrate the advantages of our approach by performing experiments with synthetic data.