"The Bayesian frame forces honesty about the prior. The frequentist frame avoids the prior by refusing to answer the question that needs one. Both are legal; the dialog between them is the citizen's mature inference skill."
What This Track Established
Six lessons of one engine: prior + likelihood = posterior. Applied to the prosecutor's fallacy (Bayes resolves it by computing the posterior explicitly with a stated prior), the medical false positive (Bayes shows the citizen panic is a base-rate-ignoring posterior misread), base-rate neglect (Kahneman's cognitive bias that Bayes is the corrective for), and sequential updating (the engine running across time as evidence accumulates).
Bayes vs Frequentist: The Mature View
The two frames are not enemies. They answer different questions with different commitments:
- Frequentist refuses to answer 'what is the probability of the hypothesis?' because the hypothesis is fixed and probability does not apply to it. Instead, it answers 'what is the probability of evidence at least this extreme, assuming the hypothesis?' This is the p-value / confidence interval / hypothesis test toolkit.
- Bayesian answers 'what is the probability of the hypothesis, given the evidence?' directly, but requires you to name a prior and accept that the posterior depends on it. This is the prior / likelihood / posterior toolkit.
The mature citizen-statistician uses both. For clean data with no prior-relevant context, frequentist tools are efficient and well-calibrated. For decisions under uncertainty with relevant base rates and accumulating evidence, Bayesian tools are honest and operational. Mixing them is also fine: many modern analyses use Bayesian models with prior selection guided by frequentist arguments.
The Cross-Reference Map
Track 06 framed the courtroom in frequentist Type I / Type II terms; Track 08 framed it in Bayesian prior / likelihood / posterior terms. Both reach the same conclusion: the legal system is designed for asymmetric protection of innocence, and the popular complaint ('why are they letting that monster walk?') ignores the cost asymmetry. Track 07 dismantled normality misuse from the frequentist tail-modeling side; Track 08 dismantles posterior misreads from the Bayesian inference side. The four tracks together (Track 04 sigma-as-lens, Track 06 courtroom, Track 07 normality-misuse, Track 08 Bayesian frame) are the citizen's full statistical lens kit.