Covid, false positives and conditional probabilities…



In courtrooms, mixing up the probability of “A given B’” with “B given A” is known as the “prosecutor’s fallacy”. In 1999, a court convicted Sally Clark of the murder of her two sons, in part because a medical expert claimed the chance of two accidental cot deaths was one in 73m. Even if this number was right – which it isn’t – it did not reflect the chance she was innocent. A double murder was also very rare: the relative likelihood of the two explanations was key and with new evidence and better statistical reasoning, an appeal court quashed the conviction.

There was controversy after a recent Observer headline referred to Bayes’s theorem as “obscure”. His ideas may be little known by the public, but they are growing among scientists. Many complex analyses done during the pandemic have been “Bayesian”, including modelling lockdown effects, the ONS infection survey, and Pfizer-BioNTech’s vaccine trial. The term “credible interval”, rather than “confidence interval”, is the giveaway.

Last week, Cass Business School announced the renaming of its institution after Bayes and his theorem. The obscure tomb in nearby Bunhill Fields is worth a visit.

Author(s): David Spiegelhalter, Anthony Masters

Publication Date: 25 April 2021

Publication Site: The Guardian