A Bayesian analysis of the Lucy Letby case: Reasonable doubt

This paper applies Bayesian inference to the Lucy Letby case under two conditional models. Model 1 assumes the prosecution's medical evidence is correct and homicides occurred. With a 0.20 prior based on five nurses with access, comparative attendance (likelihood ratio (LR) ≈ 1.67), discounted behavioural evidence (LR ≈ 2.0), and conservative post-removal mortality reduction (LR ≈ 3.5) produce a combined LR of ∼11.7, yielding a central posterior of approximately 75% (rising to ∼97% under prosecution-favourable assumptions). Model 2 adopts the 2025 Shoo Lee expert panel's conclusion that no reliable evidence supports homicide. Using a base rate prior of 3 × 10 −7 for a healthcare serial killer among NHS nurses, neutral attendance, modest behavioural support (LR ≈ 2.0), exculpatory insulin findings (LR = 0.125), and confounded post-removal data (LR ≈ 4.0) yield a combined LR near 1.0 and a posterior of approximately 0.00003% (defensible range 0.000015%–0.00024%). The roughly 660,000-fold prior divergence highlights the critical role of independently establishing the actus reus. The analysis identifies base-rate neglect, Texas sharpshooter, prosecutor's fallacy, and causal confounding as key risks, underscoring that statistical evidence cannot substitute for robust medical determination of whether crimes occurred.