🤖 AI Summary
该研究探讨了在什么条件下统计上可以区分科学相关性，通过定义相关性-分辨率指数并建立最小最大下界的方法来解决这一问题。
📝 Abstract
Statistical precision and scientific relevance operate on different scales. In regular problems, sampling uncertainty contracts at rate $n^{-1/2}$, whereas the magnitude below which an effect is scientifically negligible may be fixed or may vary with information. Let $Δ_n$ denote a relevance threshold and $I_0$ Fisher information in a regular scalar model, and define the relevance-resolution index $λ_n=\sqrt{nI_0}Δ_n$. For separated negligible and meaningful parameter classes, we establish the minimax lower bound $\liminf_{n\to\infty}R_n^*\ge 2\{1-Φ(\varepsilonκ)\}$ when $λ_n\toκ$. If $λ_n\to0$, the experiments merge and consistent classification is impossible. If $λ_n\toκ\in(0,\infty)$, the problem converges to a nondegenerate Gaussian-shift decision problem: nontrivial discrimination is possible, but consistency is not. If $λ_n\to\infty$, consistent classification is attainable under a uniform estimation-resolution condition. For $Δ_n=dn^{-γ}$, the critical rate is $γ=1/2$. We also show that moving asymmetric relevance regions are governed by standardized distances to their two boundaries rather than by total width alone. For heterogeneous true effects, we derive a significance-saturation limit and show that point-null significance can be most selective for scientifically relevant effects at intermediate information. The framework characterizes when scientific relevance is statistically resolvable, linking effect size, power, local asymptotic theory, and practical significance through a common information scale.