{
 "schema_version": 1,
 "title": "Reproduction: Beyond First-order Asymptotics in Sequential Mean Testing",
 "emoji": "📐",
 "space_id": "snaykey/repro-seq-mean-testing",
 "paper": {
  "arxiv_id": "2606.04520",
  "openreview_id": "HMyCBL2yMV"
 },
 "tags": [
  "icml2026-repro",
  "paper-HMyCBL2yMV"
 ],
 "updated_at": "2026-07-25T18:00:00+00:00",
 "root": {
  "slug": "index",
  "title": "Reproduction: Beyond First-order Asymptotics in Sequential Mean Testing",
  "file": "pages/index.md",
  "children": [
   {
    "slug": "executive-summary",
    "title": "Executive summary",
    "file": "pages/executive-summary/page.md",
    "children": []
   },
   {
    "slug": "claim-1-theorem-4-2-empirical-klinf-clt",
    "title": "Theorem 4.2 establishes a central limit theorem for the empirical KL_inf statistic, showing sqrt(n)(KL_inf(q_hat_n, m_o) - KL_inf(q, m_o)) converges in distribution to N(0, sigma^2(q, m_o)) (Theorem 4.2).",
    "file": "pages/claim-1-theorem-4-2-empirical-klinf-clt/page.md",
    "children": []
   },
   {
    "slug": "claim-2-theorem-4-4-stopping-time-clt",
    "title": "Theorem 4.4 extends this result to the stopping time tau_alpha, proving sqrt(log(1/alpha))(tau_alpha/log(1/alpha) - 1/KL_inf(q,m_o)) converges to a Gaussian limit N(0, sigma^2_bd(q,m_o)) as alpha to 0 (Theorem 4.4).",
    "file": "pages/claim-2-theorem-4-4-stopping-time-clt/page.md",
    "children": []
   },
   {
    "slug": "claim-3-dual-decomposition-anscombe",
    "title": "The proof decomposes the normalized KL_inf statistic into a term from the dual optimization (shown to vanish in probability) and a standard empirical-mean term that converges to Gaussian, combined with verification of Anscombe's condition to transfer the CLT to the stopping time (Section 4).",
    "file": "pages/claim-3-dual-decomposition-anscombe/page.md",
    "children": []
   },
   {
    "slug": "claim-4-proposition-4-5-single-run-ci",
    "title": "Proposition 4.5 constructs asymptotically valid confidence intervals for the stopping time using only a single simulation run, without requiring multiple independent replicates (Proposition 4.5).",
    "file": "pages/claim-4-proposition-4-5-single-run-ci/page.md",
    "children": []
   },
   {
    "slug": "claim-5-beta-bernoulli-crop-yield-experiments",
    "title": "Numerical experiments on synthetic Beta and Bernoulli distributions and on real crop-yield data show empirical stopping-time distributions converging to the theoretical Gaussian limit, with stronger agreement at smaller significance levels alpha (Section 5).",
    "file": "pages/claim-5-beta-bernoulli-crop-yield-experiments/page.md",
    "children": []
   },
   {
    "slug": "conclusion",
    "title": "Conclusion",
    "file": "pages/conclusion/page.md",
    "children": []
   }
  ]
 },
 "agent_view_tokens": 2211,
 "revision": "1784415979979314200"
}