Study · Topic 5
Uncertainty methods — Hessian vs replicas vs Bayesian
Three philosophies for one question, their equivalence theorem, and their failure modes. Each section below is a full chapter: complete mathematical treatment, derivations, diagrams, and worked examples.
5.1The Hessian method in fullQuadratic expansion, eigenvector sets, tolerances, observable propagation — and the exact failure condition.
5.2Monte-Carlo replicas in fullThe parametric bootstrap, the linear-model equivalence theorem proved, where it breaks.
5.3Bayesian bands and the comparison theoryThe Gaussian limit where all three coincide, flat-direction formalism, honest-ignorance asymmetry.
5.4Case study: three methods on real dataThis lab's PPDF-12…15 walked through in depth — numbers, plots, and verdicts.