The Bayesian framework — posterior probability of guilt does not meet threshold
Prosecution claim
The Crown presented the statistical evidence at trial as overwhelming, inviting the jury to conclude that the pattern was inconsistent with innocence.
Counter-evidence
A formal Bayesian statistical analysis combines the prior probability of the prosecution hypothesis, the likelihood of observed evidence under each hypothesis, and produces a posterior probability of guilt. Prof. Norman Fenton's sustained Bayesian analysis demonstrates that: the prior probability of an unprecedented cluster of deliberate neonatal air embolism acts is extraordinarily low; the likelihood of observed evidence under natural-cause alternatives (sepsis, NEC, thrombosis, outbreak conditions) is high; the posterior probability of guilt calculated on Bayesian principles does not meet the criminal-law beyond-reasonable-doubt threshold. This is not a speculative critique — it is what a formal statistical analysis of the available evidence produces. Sir David Spiegelhalter's public-communication framework, Prof. Jane Hutton's operational analysis, and Prof. Leila Schneps's Math on Trial framework each converge on the same conclusion.
Bayesian statistical analysis of the Letby evidence does not support the Crown's inference. Low prior, high natural-cause likelihood, modest prosecution-hypothesis likelihood — posterior probability of guilt is low, not the high-confidence inference the criminal standard requires.
What the jury heard
The Crown's statistical framing as if it were Bayesian in force but without the formal framework that would require alternatives to be modelled. No qualified statistician gave evidence for the prosecution.
What the Panel says
The Panel's medical finding that natural causes are sufficient on every indicted case is the substantive input the Bayesian framework requires: high likelihood of observed evidence under the natural-cause alternatives.
What independent experts add
- Prof. Norman Fenton is the UK's leading academic in Bayesian networks for legal evidence.
- The statistical-community consensus is that the Crown's framing fails Bayesian scrutiny.
- No body of peer-reviewed post-Panel statistical work defends the Crown's framing.
- Spiegelhalter's framework specifically warns against denominator-suppression and prosecutor's-fallacy presentation.
- Hutton's operational framework identifies the specific Letby chart failures: denominator, null model, attendance-rate conflation.
- Schneps's Math on Trial catalogues four specific fallacies each present in the Letby chart.
- Bayesian analysis is not speculative; it is the formal statistical framework the Royal Statistical Society has endorsed for evidence evaluation since the post-Clark guidance.