Lucy Letby: Guilty or Innocent - a Bayesian analysis

Mathematician Richard Gill (a colleague and friend) put out a tweet with a number of assumptions abou the case of Lucy Letby (the UK nurse convicted in 2023 of multiple baby murders), using a Bayesian analysis to conclude that a sepsis outbreak was much more likely to have been the cause of the baby deaths than Lucy. He claimed that, with his assumptions the posterior odds of sepsis outbreak rather than Lucy being the killer was about 4000:1. Using a simply Bayesian network I show that the posterior odds are more like 166:1 (if I have understood Richard's assumptions). Of course the critical assumptions Richard makes (which were not accepted during the trial) are that a) there was little evidence of malicious harm to the babies; and b) there was much evidence of a sepsis outbreak. Whether or not these assumptions are reasonable this is nevertheless a nice example of a Bayesian network in action