fix: clamp KDE bandwidth to the plotting domain, not absolute units
Small districts produce rare-event count posteriors that are heavily zero-inflated, and the absolute 1e-3 floor / raw-sd fallback broke on both extremes of that data: - All-identical draws (e.g. 500 zeros, the norm for a group with a handful of students) collapsed to h = 1e-3, a near-delta spike of density ~399. Because SexRidgeColumn shares one maxPdf per column, that single spike flattened every other ridge in the column to sub-pixel height. Measured on a real district (0400315 AZ, unified_m4_mod): the three informative ridges rendered at 0.07-0.13px of a 47.56px row. - When IQR is 0 -- the normal case when most draws are 0 -- min(sd, iqr/1.34) was falsy and the rule fell all the way back to raw sd, which a few extreme draws inflate until the ridge is a flat line claiming maximal uncertainty. Bandwidth is now clamped to [domainWidth/50, domainWidth/6] and the robust rule degrades by picking the smallest *positive* spread estimate instead of discarding robustness entirely. The floor is slightly wider than one render step at n = 60, so a degenerate draw set resolves as a narrow bump; it does not bind on an ordinary posterior (spread wider than ~8% of the domain keeps its own Silverman bandwidth). On the district above the informative ridges now render at 5.66-5.70px, a ~60x improvement. Five new tests cover both failure modes; all five fail against the old formula.
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+45
-8
@@ -6,7 +6,20 @@
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*/
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const SQRT_2PI = Math.sqrt(2 * Math.PI)
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// Absolute last-resort floor, used only when no plotting domain is known.
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const MIN_BANDWIDTH = 1e-3
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// Bandwidth is clamped relative to the plotting domain, not to absolute units,
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// because these draws are rate-per-1,000 values whose scale varies by orders of
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// magnitude between districts. domainWidth/50 is slightly wider than one render
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// step at the charts' n = 60 (step = domainWidth/59), so a degenerate draw set
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// (e.g. 500 identical zeros, common for small districts) resolves as a narrow
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// bump instead of a delta spike that flattens every other ridge sharing the
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// column's maxPdf. It is also loose enough not to bind on an ordinary posterior:
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// a spread wider than ~8% of the domain keeps its own Silverman bandwidth.
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// domainWidth/6 stops a handful of extreme draws from inflating sd until the
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// curve is a flat line.
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const BANDWIDTH_FLOOR_DIVISOR = 50
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const BANDWIDTH_CEILING_DIVISOR = 6
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/**
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* Linear-interpolated quantile (R type-7). Does not mutate `draws`.
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@@ -32,19 +45,40 @@ function standardDeviation(draws) {
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}
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/**
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* Silverman's rule-of-thumb bandwidth (robust variant using min(sd, IQR/1.34)),
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* floored so a near-degenerate draw set (e.g. almost all zeros) never
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* collapses the kernel to a spike.
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* Silverman's rule-of-thumb bandwidth (robust variant using the smallest
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* *positive* spread estimate among sd and IQR/1.34), clamped to a fraction of
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* the plotting domain.
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*
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* Both ends of the clamp matter for the zero-inflated count posteriors small
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* districts produce. Without the floor, an all-identical draw set (sd = IQR = 0)
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* collapses to a delta-function spike. Without the ceiling, a group whose IQR is
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* 0 (the normal case when most draws are 0) falls back to raw sd, which a
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* handful of extreme draws inflates until the ridge is a featureless flat line.
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*
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* @param {number[]} draws
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* @param {number} [domainWidth] - width of the x-range the curve will be drawn
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* over. Omit only when no domain is known; the clamp then degrades to the
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* absolute MIN_BANDWIDTH floor.
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* @returns {number}
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*/
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export function silvermanBandwidth(draws) {
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export function silvermanBandwidth(draws, domainWidth = 0) {
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const width = domainWidth > 0 ? domainWidth : 0
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const floor = width ? width / BANDWIDTH_FLOOR_DIVISOR : MIN_BANDWIDTH
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const ceiling = width ? width / BANDWIDTH_CEILING_DIVISOR : Infinity
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const n = draws.length
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if (n < 2) return MIN_BANDWIDTH
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if (n < 2) return floor
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const sd = standardDeviation(draws)
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const iqr = quantile(draws, 0.75) - quantile(draws, 0.25)
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const spread = Math.min(sd, iqr / 1.34) || sd || MIN_BANDWIDTH
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return Math.max(0.9 * spread * Math.pow(n, -0.2), MIN_BANDWIDTH)
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// Degrade gracefully: keep the robust rule when IQR is informative, use sd
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// when it isn't, and let the floor handle a fully degenerate draw set —
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// rather than treating a zero spread as "no estimate available".
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const candidates = [sd, iqr / 1.34].filter((v) => v > 0)
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const spread = candidates.length ? Math.min(...candidates) : 0
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const raw = 0.9 * spread * Math.pow(n, -0.2)
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return Math.min(Math.max(raw, floor), ceiling)
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}
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/**
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@@ -57,7 +91,10 @@ export function silvermanBandwidth(draws) {
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*/
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export function kdeCurve(draws, { min = 0, max, n = 60 } = {}) {
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const hi = max ?? Math.max(...draws) * 1.1
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const h = silvermanBandwidth(draws)
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// Guarded against a degenerate/inverted domain so the bandwidth clamp can
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// never be handed a negative width.
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const domainWidth = Math.max(hi - min, 0)
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const h = silvermanBandwidth(draws, domainWidth)
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const step = (hi - min) / (n - 1)
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const points = []
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for (let i = 0; i < n; i++) {
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