Prof. Norman Fenton — Bayesian analyses of the Letby case (blog posts 2023–2026)

A summary of Prof. Norman Fenton's sustained academic-blog series on the Letby case from late 2023 onwards. Fenton applies the formal Bayesian network framework to the evidence, modelling prior probability of the prosecution hypothesis, likelihood of observed evidence under each hypothesis, and posterior probability of guilt. His conclusion is that posterior probability does not meet the criminal-law threshold. This is the most detailed publicly-available Bayesian analysis of the Letby evidence.

Last updated 2026-04-22

14 min read

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.