When you have eliminated the impossible, whatever remains, however improbable, must be the truth. So wrote Arthur Conan Doyle in his Sherlock Holmes novels.
Holmes’ approach to crime-busting was simple: develop a set of potential answers and then evaluate them with each and every piece of evidence he could find. Starting with a broad set of possible explanations to a problem might make life more difficult initially; but the genius of Holmes was to narrow down his possible solution space ruthlessly and systematically.
Applying this mindset of critical evaluation can be incredibly useful in finding answers to a wide range of complex problems. However, in reality, people are wonderful beings who make decisions based on a melting pot of emotion, experience, mood and other psychological factors. Sifting, sorting and synthesising evidence, without introducing a range of biases, is difficult without some form of cognitive scaffolding.
The good news is that there is a well-established approach that does exactly that. Bayesian statistics provides a useful framework to refine initial beliefs (starting with an a priori probability) on the basis of each new element of data to reach a conclusion (called the posterior probability). Elementary, as Holmes might have said.
Perhaps surprisingly – and despite being formulated over 250 years ago by a statistically-minded British clergyman – practical application of the Bayesian approach can be contentious. One particular example is in real life criminal investigations and jury trials where evidence is often accumulated and presented selectively. Indeed, the UK Court of Appeal has previously been critical on the use of Bayesian techniques when applied to challenge stated statistical probabilities on DNA matches. This apparently stems from a desire to keep things simple for the jury but can present real problems in the misuse of evidence when taken in isolation. To reach a verdict that is beyond reasonable doubt, surely jurors deserve to have access to all relevant information?
The systematic use of Bayesian statistics could also help speed up complex criminal investigations by structuring evidence more rigorously; considering a wide range of hypotheses; and then rapidly winnowing those down to the most likely answer.
It might seem improbable that the work of an 18th century Presbyterian Minister and a 19th century whodunnit novelist can help unlock the darkest mysteries of 21st century crime. But it is certainly not impossible.