bayesFactorThreshold_cost
plain-language theorem explainer
The theorem establishes that the J-cost of the barely-convincing Bayes factor threshold equals phi minus three-halves. Bayesian statisticians applying Recognition Science to evidence thresholds would cite it to anchor the minimum detectable update at the golden-ratio fixed point. The proof is a one-line wrapper that unfolds the threshold definition and invokes the precomputed J-cost value at phi.
Claim. The J-cost of the barely-convincing Bayes factor threshold equals $phi - 3/2$.
background
The module develops Bayesian updating from J-cost, where posterior probability is proportional to likelihood times prior and information gain is measured by KL divergence. Recognition Science predicts that the minimum detectable update (the step from unchanged to meaningfully updated beliefs) occurs at a J-cost of J(phi) approximately 0.118 on the likelihood ratio. The Bayes factor threshold is defined as the canonical barely-convincing value B = phi, with moderate evidence at B = phi squared. Upstream, Jcost_phi_val states that J(phi) = phi - 3/2 exactly, using phi squared equals phi plus one.
proof idea
The proof is a one-line wrapper that unfolds the definition of bayesFactorThreshold to phi and then applies the lemma Jcost_phi_val.
why it matters
This anchors the Bayesian evidence thresholds inside the Recognition Science framework by linking the minimum detectable update directly to the phi fixed point from the forcing chain (T6). It supports the structural theorem on Bayesian updates from J-cost and aligns with Kass-Raftery (1995) definitions of positive evidence for factors in (3,10). It touches the open empirical question of whether subjectively convincing thresholds consistently fall inside (1.5,4.0).
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