Energy-biased detection probability ($P(i\mid D)=p_i{\eta }_i/{\sum }_j{p}_j{\eta }_j$)

If source class $i$ has prior fraction $p_i$ and detection efficiency ${\eta }_i$, its fraction among detected events is proportional to $p_i{\eta }_i$. Bayes' theorem normalizes these products. Class-dependent losses therefore bias the detected composition even when the incident fractions are known exactly.