Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.gibbs-failures

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/gibbs_failures.clj1 definitions, 4 theorems

AHoF V23 Gibbs Sampling (Failures): reuse the Gibbs structure over the failure region, resampling each variable from its full conditional; the draw is from the conditional when the uniform sample falls under the conditional mass: draws-conditional? draw conditional-mass = decide (draw <= conditional-mass). Proved native and axiom-free (decision, two positive instances, at-most certificate, negative instance). Requires audit/decide-nnrat-at-most, nnrat/at-most, nnrat/decide-at-most-true-sound (all in the D63 checkpoint). Scope (measured by the kernel): this module has 4 worked instances (statements about specific values). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.gibbs-failures` prints this classification.

gibbs-fail/draws-conditional? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

gibbs-fail/draw-under-mass :
  → ce-is/elite? 1/4 1/2 = data/true

gibbs-fail/boundary-draw :
  → ce-is/elite? 1/2 1/2 = data/true

gibbs-fail/conditional-certificate :
  → 1/4 ≤ 1/2

gibbs-fail/draw-over-mass :
  → ce-is/elite? 3/4 1/2 = data/false