I watched the pilot episode A Study in Pink of the BBC television series Sherlock. It made me wonder if Sherlock Holmes is even theoretically possible. This is not just a fanciful question: if what Sherlock Holmes is doing can be done, but it too difficult for humans to do in practice, then eventually we can build machines that will give the police the powers of Sherlock Holmes.
The Sherlock Holmes formula, from a Bayesian perspective, consists of copious amounts of observation coupled with strong assumptions on the likelihood and occasionally strong prior assumptions to resolve an ambiguity. My question is whether the observations actually contain as much information as Sherlock says, i.e., is the likelihood (or prior) terribly misspecified?
For instance, in A Study in Pink Sherlock concludes that the owner of a cell phone is a habitual drunk on the basis of extensive scratching found near the power plug on the phone: ``only a habitual drunk has consistently shaky hands when plugging in their phone at night.'' But is that true? If we were to survey millions of cell phones, select the ones with extreme scratching around the power plug, and then look at the proportion of habitual drunks in the resulting owner population, what would we find relative to the proportion of habitual drunks amongst all cell phone owners?
In any event there are enough known problems with human reasoning, e.g. confirmation bias, that a future computerized police assistant will probably greatly improve detective work, even if correct extrapolations from small observations are not achievable.
Also, the show is really well done.