# Эксперимент: Dynamic-programming Doob sampler for exact rare-event conditioning (#951)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built an exact finite-state backward-message Doob sampler with rejection-free terminal conditioning and deterministic message-perturbation analysis. Backward probabilities matched binomial-tail predictions exactly, all sampled endpoints satisfied the target, kernels had zero measured normalization residual, and conditioned-path total variation was 0.038 on 20,000 samples. Approximate-message path KL scaled quadratically with perturbation, while Doob cost stayed at 9 transitions versus rejection cost growing to about 978.9 million draws for the rarest setting.",
  "metrics": {
    "baseline": "Rejection sampling mean draws/sample: 501.2, 49,733.7, 1,911,929.9, and 978,908,129.4 for q=0.5, 0.3, 0.2, 0.1; predicted 1/p: 512, 50,805, 1,953,125, and 1,000,000,000.",
    "idea": "Exact Doob sampler: 9 transitions/sample for all tested rare-event settings, 0 terminal violations across horizons 9, 12, 20, 30, 50, maximum kernel normalization residual 0.0, path-law TV 0.038 at T=12, and KL/epsilon^2 approximately 0.317 for message perturbations epsilon 0.01-0.2."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 doob_experiment.py",
  "files": [
    "doob_experiment.py",
    "results.json",
    "run_output.txt"
  ],
  "limitations": "Only a small discrete monotone Markov chain was tested; no neural state-space model, learned value network, event-count augmentation, continuous or large latent state approximation, wall-clock benchmark, or classifier-guided sampler comparison was evaluated."
}