One way of thinking of this process is that we are ‘reversing the order’ of the tree to put testing first, followed by the revelation of the truth. This is shown explicitly in Figure 11.3. This ‘reversed tree’ arrives at exactly the same numbers for the final outcomes, but respects the temporal order in which we come to know things (testing and then the truth about doping), rather than the actual timeline of underlying causation (doping and then testing). This ‘reversal’ is exactly what Bayes’ theorem does – in fact Bayesian thinking was known as ‘inverse probability’ until the 1950s.
