If an athlete tests positive for performance-enhancing drugs, what is the probability that he or she is actually doping? If police increase foot patrols in an urban neighborhood but property crime increases anyway, should the foot patrols be declared ineffective and discontinued?
In an oil and gas context, suppose you drill one of two fault blocks which are adjacent to your producing field and you find it to be hydrocarbon-bearing. By how much should you increase your chance of success for the other block? If you run a well test and the results indicate that the reservoir compartment is large, how sure should you be that the compartment is, in fact, large?
“Bayesian logic” may sound arcane, but it is critical to correctly incorporating new information into our view of the world (or reservoir). It is even how one explains the infamous Monte Hall problem, in which a contestant who has chosen a b
ox (which may or may not contain a prize) has to decide whether to trade for a different box.