Wilcoxon + FDR superposed-epoch demo

Interactive companion to Constraints on the interpretation of atmospheric potential gradient anomalies associated with earthquakes: Evidence from Peru and Argentina — Romero et al. (2026).

This simulator reproduces the statistical framework of Section 4.3 of the paper. It generates synthetic earthquake-centered PG' data with parameters matched to the observed CAS / ICA backgrounds and shows how the Wilcoxon signed-rank test combined with BH-FDR correction detects (or fails to detect) injected anomalies of varying amplitude, duration, and lag.

Quick orientation. Each row of the heatmap = one earthquake (n events total). Each column = one relative day from −90 to +15 (106 days). The colour shows the event-level daily median PG' (red = positive, blue = negative). The Wilcoxon test runs independently at each of the 106 days. Day 0 is highlighted because it is the focal lag in the precursor literature, but a real anomaly at any day would be flagged.

1. Controls

Number of events (n) 117

Background sigma (V/m, daily medians) 14.0

Random seed 42

Anomaly amplitude (V/m, signed) 0.0

Anomaly center day (relative) -2

Anomaly duration (days continuous) 3

Fraction of events showing anomaly (%) 100

FDR alpha 0.05

Action

2. Heatmap (events × relative day)

3. Composite day-level median + Wilcoxon significance

4. −log10(p) per day with FDR threshold

5. How to interpret

Composite day-level median (panel 3, dark line): median of event-level daily medians across all events, computed independently at each relative day. Red shading = pre-seismic window [−15, 0]. Vertical dashed line = day 0.
Stars on composite: days where Wilcoxon FDR-corrected q < alpha. These are the only "reliable" anomalies. Uncorrected p < alpha (without FDR) is shown as smaller dots — about 5 such days are expected by chance across 106 tests under the null.
Panel 4: −log10(p_raw). Horizontal lines = uncorrected α and FDR threshold. A real anomaly produces a tall narrow spike at the affected lags; null produces scattered low bars.
The MDE for n=117 with sigma=14 is approximately 4 V/m. Try Preset 2 (−5 V/m): may or may not survive FDR depending on duration. Preset 3 (−15 V/m): always survives.

6. Pedagogical exercises

Run Preset 1 (null): confirm that q < 0.05 occurs at zero or very few days (false positives). Repeat with different seeds — the false-positive count fluctuates.
Run Preset 2 (weak pre-seismic): at amplitude near MDE the FDR may or may not catch the anomaly. Increase amplitude until detection becomes consistent.
Run Preset 3 (strong pre-seismic): detection is now robust. Try lowering the "fraction of events showing anomaly" — what fraction is needed for detection?
Run Preset 4 (single-day shift): a brief 1-day shift is detectable if amplitude is high enough. Try varying the shift amplitude to find the practical detection threshold.
Try a positive amplitude to confirm the test is two-sided.
Set duration = 30 days at amplitude = −2 V/m: a sustained but small shift may be detected by FDR even though no single day is dramatic.

Connection to Section 4.3 of P04_EQK: in our real CAS / ICA data, no configuration showed FDR-significant day 0 across 20 stratified subsets. This simulator shows you what a real signal would have looked like.