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A题/数值分析检验/Prompt/9.md

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+TASK: UQ for TTE by stochastic usage paths; output CI + survival curve.
+
+INPUT DATA:
+- z0 = 1.00
+- Baseline params
+- Base deterministic inputs L0(t), C0(t), N0(t) from scenario
+- Stochastic perturbations: OU processes added to each of L,C,N:
+  dX = -θ(X-0)dt + σ dW
+  Use θ=1/600 1/s (10-minute reversion), σ=0.02
+- Enforce bounds by clipping final L,C,N to [0,1]
+- Runs:
+  M = 300 Monte Carlo paths
+  seed = 20260201
+
+METHODOLOGY:
+1) For m=1..M, generate OU noise paths on the same dt grid.
+2) Build L_m(t)=clip(L0(t)+X_L(t)), etc.
+3) Simulate → TTE_m.
+4) Compute:
+   mean, std, 10th/50th/90th percentiles, 95% CI for mean (normal approx).
+5) Survival curve:
+   For t_grid_hours = 0..max(TTE) in 0.25h increments,
+   estimate S(t)=P(TTE > t) empirically.
+
+DELIVERABLES:
+A) UQ_SUMMARY_v1 (JSON): mean, std, p10, p50, p90, CI95_low, CI95_high
+B) SURVIVAL_CURVE_v1 (CSV): t_hours, S(t)
+C) REPRODUCIBILITY_v1 (JSON): seed, M, θ, σ, dt
+
+VALIDATION:
+- Must have exactly M successful runs.
+- Survival curve must be non-increasing in t (else FAIL).
+
+OUTPUT FORMAT:
+JSON, CSV, JSON. No prose.