Context
Prof. Norman Fenton of Queen Mary University of London has maintained a sustained academic blog series on the Letby case from late 2023 onwards. Fenton’s research area is Bayesian networks for legal evidence — the formal mathematical framework for evaluating statistical evidence in criminal trials.
The Bayesian framework applied
Fenton’s blog posts walk through the Letby statistical evidence under the formal Bayesian framework:
- Prior probability of the prosecution hypothesis.
- Likelihood of observed evidence under the prosecution hypothesis.
- Likelihood of observed evidence under the natural-cause alternatives.
- Posterior probability of guilt, calculated by Bayes’s theorem.
Each input is quantified, at least approximately, against published data. The output is a posterior probability of guilt that does not meet the criminal-law beyond-reasonable-doubt threshold.
The principal critiques Fenton develops
- Prior-probability neglect. The Crown’s case implicitly assumed a prior probability of single-nurse cluster that is not supportable on the international forensic-pathology literature.
- Selection-effect amplification. The shift-rota chart’s selection of suspicious events magnifies overlap probability artificially.
- Independence-assumption failure. The cluster events are correlated via the unit’s shared environmental and staffing conditions, not independent as the statistical calculation implicitly treated them.
- Alternative-hypothesis modelling absence. A Bayesian framework formally requires the alternative hypotheses to be modelled. The Crown’s presentation did not.
Why the Fenton framework is load-bearing
The formal Bayesian framework is not a fringe statistical position. It is the framework the Royal Statistical Society endorsed in its post-Clark guidance, the framework Sir David Spiegelhalter communicates publicly, the framework Prof. Richard Gill applied to the de Berk case. Fenton operationalises it specifically for Letby. The output does not support the Crown’s inference.
Read alongside
Prof. Norman Fenton — biography, The Bayesian framework analysis, Evidence: Bayesian framework, Statistics deep-dive.