Lume 1.2 – Method Calibration

Field Calibration Data

Live data from the mWater Lume 1.2 – 2026 Validation Data datagrid. Each water sample collection event is paired with a reference enumeration; the Method column distinguishes which reference was used — Colilert (IDEXX defined-substrate MPN), membrane filtration (MF, CFU), or compartment bag tests (CBT, MPN). The Use in Calibration column flags rows that are unusable because no /diagnostics record (water temperature, required by the CFU regression) was streaming within ±20 min of the sample. All date/time columns are displayed in UTC. Times are corrected from the mWater-stored value using the Timezone Entered column: mWater records times using the data-entry device’s local clock (Boulder, MDT = UTC−6); for samples collected in a different timezone the stored time is adjusted accordingly.

Boulder Creek E. coli Distribution — All Colilert Grabs

All unique Colilert grab samples collected at Boulder Creek sites (n = 39, deduplicated). Values in CFU/100 mL. EPA single-sample recreational threshold: 126 CFU/100 mL.

Observed vs. Predicted E. coli — Colilert (Original Empirical OLS)

Pooled OLS: log10(colilert) ~ barcode + mon2_val + temperature + tof_mean + mon2_val×temperature (led_power = 512, sipm_bias ≈ 3000, reference barcode: 50046). Left: all matched grabs. Right: post burn-in only (sensors 50052 and 50066 excluded). Source data: ⬇ field_matched_512.csv

Observed vs. Predicted E. coli — Corrected Single-Predictor Model

Sensor signal is first run through a physics-motivated correction pipeline derived from Bedell et al. 2022 (temperature) and Skinner et al. 2024 (turbidity), with ρ and k fit empirically from this field dataset rather than taken from the literature seeds:
   mon2_corrected = mon2_val · exp(−ρ · (sipm_temperature − 20)) · exp(−k · NTU),  NTU = max(0, −145.89 + 2.0488 · signal_per_spad_kcps)
Then a single-predictor OLS: log10(colilert) ~ barcode + mon2_corrected — 2 free coefficients instead of 5, sensor offsets in the FE intercept, all temperature and turbidity dependence absorbed into mon2_corrected. Fitted ρ = −0.111/°C (vs Bedell literature −0.03) and k = +0.0004/NTU (vs Skinner literature −0.004) on full data — the field Lume has a much steeper temperature dependence than Bedell measured in lab tryptophan standards, and the turbidity coefficient effectively vanishes in this drinking-water deployment.

Compared to the 4-predictor original regression directly above, this 1-predictor corrected model achieves essentially equivalent in-sample R² on post-burn-in data (0.68 vs 0.66) and is far less overfit: the original's standard LOO R² is −0.92 on the full dataset (worse than predicting the mean); the corrected model's standard LOO is 0.43.

Two LOO numbers are reported because ρ and k were tuned from the data, and a fair generalization check has to account for that. Standard LOO refits only the OLS coefficients per fold (ρ and k stay at their full-data values, so they leak into every fold). Nested LOO refits ρ and k inside each fold as well — the rigorous measure. The nested LOO is meaningfully lower (0.31 full / 0.29 post-burn-in) because the fitted ρ wanders ±0.02 across folds; that instability is real and is what the page now displays as the honest generalization stat. The empirically-fit ρ tells us the Lume's effective temperature sensitivity in the field is roughly 3.7× stronger than what Bedell measured for a pure tryptophan standard in the lab — consistent with the field signal including SiPM gain drift and UV LED output drift on top of fluorophore quenching. With N = 37 and 6 effective parameters (intercept + 4 sensor FE + slope + ρ + k), the model is at the threshold where more data is the only real remedy for the remaining nested LOO gap.

Binary Detection: ≥126 CFU/100 mL — Original 4-Predictor Logistic + Sensor FE

Logistic regression: features mon2_val, temperature, tof_mean, mon2_val×temperature (z-scored per LOO fold) plus barcode fixed effects (reference: 50046). Left: all matched grabs. Right: post burn-in only. Metrics computed via LOO-CV. Source data: ⬇ field_matched_512.csv

Binary Detection: ≥126 CFU/100 mL — Corrected Single-Predictor Logistic + Sensor FE

Same logistic regression with the same Bedell + Skinner correction pipeline as the corrected OLS above. Single continuous feature mon2_corrected (z-scored per LOO fold) plus barcode fixed effects (reference: 50046). One free continuous coefficient instead of four. Empirically-fit ρ and k from the OLS section are reused.

Lab Calibration Data

Jan 2–6, 2026 calibration sessions (paper training range). Fluorescence signal (mon2_val) at the paper operating point: led_power = 1024, sipm_bias = 3040. CBT calibration data is in the field-calibration table above.
⬇ Download full dataset (CSV)

Lab: Predicted vs. Observed — Operating Point Comparison

Pooled OLS (Jan 2–6, n = 125): log₁₀(colilert) ~ barcode + signal × floor_temp × tof_mean. Barcode is a fixed-effect intercept shift (reference: 50030); slopes shared. Fit separately for each LED/bias operating point. In-sample R².

Lab Binary Logistic — ≥126 CFU/100 mL

Logistic regression trained on the full lab dataset (Jan 2–21 2026, n = 300 rows with valid production-combo readings), binary label: Colilert ≥ 126 CFU/100 mL. Features: mon2_val_512, floor_temp, tof_mean (all z-scored; no sensor fixed effect so the model is sensor-agnostic). Performance estimated by leave-one-out cross-validation (LOO-CV): each fold re-standardizes from the training set of n = 299 before predicting the held-out row. Note: the 9 positive examples all come from one contamination event (Jan 8, three consecutive time points). LOO-CV performance for the positive class may be over-optimistic due to temporal correlation between the 9 rows.

Merged Lab + Field Binary Logistic — ≥126 CFU/100 mL

Logistic regression fit on the combined lab (Jan 2–21 2026, n = 300) and field (n = 30) datasets. Binary label: Colilert ≥ 126 CFU/100 mL (16 positives total: 9 lab, 7 field). Features: mon2_val, temperature, tof_mean (continuous, z-scored per LOO fold) plus a dummy variable for every sensor relative to reference 50030 (unscaled 0/1). All 9 sensors are included. Field sensors with very few samples (50052 n=2, 50062 n=1, 50066 n=1) have sparse dummy estimates; their LOO predictions fall back to the pooled signal when their dummy is unobserved in training.