Spaces:
Running
Running
File size: 2,930 Bytes
1b42967 655d378 3323ff3 655d378 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 | {
"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"
}
|