Measurements of low-level radioactivity often give results of the order of the detection limit. For many applications, interest is not only in estimating activity concentrations of a single radioactive isotope, but focuses on multi-isotope analyses, which often enable inference on the source of the activity detected (e.g. from activity ratios). Obviously, such conclusions become questionable if the measurement merely gives a detection limit for a specific isotope. This is particularly relevant if the presence of an isotope, which shows a low signal only (e.g. due to a short half-life or a small transition probability), is crucial for gaining the information of interest. This paper discusses a new approach which has the potential to solve these problems. Using Bayesian statistics, a method is presented which allows statistical inference on nuclide ratios taking into account both prior knowledge and all information collected from the measurements. It is shown that our method allows quantitative conclusion to be drawn if counts of single isotopes are low or become even negative after background subtraction. Differences to the traditional statistical approach of specifying decision thresholds or detection limits are highlighted. Application of this new approach is illustrated by a number of examples of environmental low-level radioactivity measurements. The capabilities of our approach for spectrum interpretation and source identification are demonstrated with real spectra from air filters, sewage sludge and soil samples.