Biased showers: A common conceptual framework for the interpretation of high-$P_T$ observables in heavy-ion collisions

After the start of the LHC, a plethora of novel observables for jet tomography in heavy-ion collisions has appeared. Many of these studies have yielded counter-intuitive null results of apparently unmodified jets, which have sparked (sometimes exotic) theoretical efforts to explain these findings. However, it has to be realized that almost all current high P_T observables measure conditional probabilities of events, not probabilities. Thus, the correct starting point for their theoretical understanding is Bayes' formula, and the biases introduced by the conditioning are crucial to understanding the outcome. Once this is introduced properly into the modelling process, the counter-intuitive results are seen to find a natural explanation in terms of various biases and the puzzles largely disappear. In this work, a conceptual framework to classify the various observables according to the types of bias they are sensitive to is presented and illustrated with a large number of case studies ranging from simple jet finding to 2+1 dihadron triggered correlations.