Bayesian: the word that buys regulatory credibility without earning it

What Bayesianism really is

Thomas Bayes formulated that probability is not a frequency but a state of belief. P(A|B) = P(B|A) × P(A) / P(B). The prior, the likelihood, the posterior — an engine for updating knowledge.

In medicine, this philosophy is natural. A clinician performs intuitive Bayesianism: pre-test probability, test result, revised diagnosis.

The genuine virtues

Rare data (HDLSS), uncertainty quantification (distribution vs point score), integration of causal knowledge as directed graphs. The FDA and EMA recognise the value of this approach.

The DAG, the causal graph — and the fatal confusion

An arc in a Bayesian network does not say “A causes B.” It says “if I observe A, I must revise my belief about B.” Judea Pearl distinguishes three levels: observing, intervening, imagining. A Bayesian network operates at the first level. A causal graph at all three.

What start-ups actually do

Maximum likelihood estimation, uniform or conjugate priors for convenience, uncertainty not propagated. The result looks Bayesian, sells as Bayesian, but lacks the properties.

A globally calibrated model can be catastrophically miscalibrated locally. Silent drift renders the model inadequate without alarm.

The HR argument

A senior data scientist mastering transformers costs €80–140k. A biostatistician mastering Bayesian networks costs €50k. The architectural choice is partly an HR choice.

What should be demanded

Independent clinical validation. Honest uncertainty characterisation. Drift monitoring procedure. A team capable of maintaining the model over time.

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Key takeaways

The fundamental distinction: frequentists estimate fixed parameters; Bayesians update beliefs. You cannot be 'a little bit' Bayesian.
Start-ups use Bayesian networks as a graphical formalism but estimate via maximum likelihood with priors chosen for computational convenience.
The yellow fingers example: a learned Bayesian network would include a yellow fingers → cancer arc. But intervening on yellow fingers has no effect — correlation vs causation confusion.
A globally calibrated model can be catastrophically miscalibrated locally. Silent drift renders the model inadequate without alarm.
The HR argument: architectural choice is partly a recruitment choice disguised as a technical decision.