Candidate RELSA zones from a score density

The primary foRcast paper explores local minima of a Gaussian KDE over longitudinal RELSA scores. These valleys describe the sampled score distribution. They do not establish transitions between normal welfare and distress. The legacy output names normal, attention, danger are descriptive labels only.

Kernel, bandwidth and implementation differences

bw_nrd0() uses R's rule 0.9 * min(sd, IQR/1.349) * n^(-1/5) with the zero-spread fallback. The official R density documentation uses a Gaussian default, 512 grid points and an extent of three bandwidths beyond the data. R performs an FFT-based approximation and its old.coords compatibility option changes historical behavior. The Python helper evaluates SciPy's Gaussian KDE directly, with an analytic Gaussian for constant samples. It matches the bandwidth convention, not bitwise R density output or the paper's exact thresholds. SciPy's named silverman bandwidth factor is a different convention and must not be substituted silently.

Input scores must be nonnegative. Missing scores are omitted. Fewer than two finite scores cannot define a KDE. Constant samples produce no usable interior threshold. A bandwidth must be finite and positive. n_thresholds is a maximum count, not a demand to invent boundaries. The default min_zone_fraction=0.02 removes minima isolating fewer than 2% of observations; this is a local heuristic, not a published or welfare-validated cutoff. Set it to zero to inspect raw minima. Zone assignment includes equality in the higher zone; threshold JSON preserves full precision so its decisions agree with CSV labels.

The paper gives sepsis thresholds 0.337/0.643 in Results/Figure 3 but 0.337/0.647 in the abstract. These are historical model-specific observations, not transferable clinical limits. Earlier skill notes included full-cohort reproduction and bandwidth-sweep numbers; those analyses are not repeated by this refresh and are not presented as current execution evidence.

Population and sampling are part of the model

Use a development population that represents the intended comparison: endpoint animals, survivors and controls where scientifically appropriate. Explain exclusions, baseline-row inclusion, measurement cadence, variable panel and reference scale. More frequent observations and longer-lived animals contribute more KDE mass. Endpoint-related truncation changes that mixture; 239 measurements from seven animals are not 239 independent animals.

Sensitivity analyses should vary bandwidth, sampling/aggregation and baseline inclusion; assess threshold stability with animal-level resampling or held-out cohorts. Pool only measurements sharing one calibration and measurement interpretation. Select thresholds on development data and freeze them before evaluation. Candidate zones cannot be tuned until held-out endpoint classification looks favorable.

Runnable synthetic workflow

After the scoring command in SKILL.md, run from the skill directory:

python scripts/kde_thresholds.py relsa_scores.csv --n-thresholds 2 \
  --plot zones.png --json zones.json --label-out zoned.csv

for f in 0.8 0.9 1.0 1.1 1.2; do
  python - "$f" <<'PY'
import sys, pandas as pd
sys.path.insert(0, "scripts")
from kde_thresholds import find_thresholds, bw_nrd0
v = pd.read_csv("relsa_scores.csv")["relsa"].dropna()
bw = bw_nrd0(v.to_numpy()) * float(sys.argv[1])
print(sys.argv[1], [round(t, 3) for t in find_thresholds(v, bandwidth=bw).thresholds])
PY
done

An empty result is legitimate. Do not keep shrinking bandwidth until minima appear. A stable minimum still needs independent welfare relevance; a bimodal sampling mixture alone can create it. The official R relsa_levels path was source-reviewed but not executed here, so it is not a tested fallback. Animal-level RELSA maxima used in the original paper's clustering are a different quantity from all-time-point KDE inputs.

Welfare and regulatory interpretation

The European Commission severity assessment framework addresses prospective classification, monitoring during procedures and actual experienced severity. The Directive uses non-recovery, mild, moderate and severe categories with procedure-specific assessment. No reviewed official guidance maps a RELSA value or KDE zone directly to these categories. A KDE output cannot replace the approved humane endpoint criteria or assessment by responsible personnel. No low score, empty threshold list or reassuring forecast establishes permission to wait when observed welfare signs require action. Record that distinction in reports.