=== versions ===
python 3.12.0 | scikit-learn 1.9.1 | scipy 1.18.1 | rasterio 1.5.2 | contextily 1.7.1 | geopandas 1.2.0

=== data (same cleaning as Part 1) ===
snapshot uploaded 26 October 2026: 27,552 council trees in the borough, 3,292 London planes
grid: 305 x 267 cells of 25 m, 34,847 inside the borough

=== bandwidth selection ===
scipy gaussian_kde: Scott factor 0.2593, Silverman factor 0.2593
  kernel standard deviation (from the data covariance): 470 m east-west, 417 m north-south
scikit-learn KernelDensity(bandwidth='scott').bandwidth_ = 0.259 -> read as metres on raw coordinates: standardise first or pass a number
likelihood cross-validation (5-fold, 25 bandwidths from 10 to 1,000 m): best h = 32 m
  h =     10 m: mean held-out log-likelihood -18.333 per tree
  h =     22 m: mean held-out log-likelihood -15.687 per tree
  h =     46 m: mean held-out log-likelihood -15.709 per tree
  h =    100 m: mean held-out log-likelihood -16.136 per tree
  h =    215 m: mean held-out log-likelihood -16.564 per tree
  h =    464 m: mean held-out log-likelihood -16.919 per tree
  h =   1000 m: mean held-out log-likelihood -17.335 per tree
fixed planning distance: Epanechnikov kernel, radius 400 m (same spread as a Gaussian with sd 163 m)
Scott/Silverman (Gaussian, sd 470 × 417 m): peak 3.3 planes/ha, 99th percentile 3.1, share of the kernel mass inside the borough 0.818
likelihood CV (Gaussian, sd 32 m): peak 37.4 planes/ha, 99th percentile 15.0, share of the kernel mass inside the borough 0.980
planning distance (Epanechnikov, radius 400 m): peak 5.3 planes/ha, 99th percentile 4.4, share of the kernel mass inside the borough 0.913

=== kernel comparison at the same spread (sd 100 m per axis) ===
    gaussian: h =   100 m, peak   9.7 planes/ha, correlation with Gaussian r = 1.000
epanechnikov: h =   245 m, peak   8.7 planes/ha, correlation with Gaussian r = 0.990
      tophat: h =   200 m, peak   8.4 planes/ha, correlation with Gaussian r = 0.967
 exponential: h =    58 m, peak  13.5 planes/ha, correlation with Gaussian r = 0.977

=== sample weights: crown area ===
3,288 of 3,292 planes have a crown spread > 0 (median 11 m); total crown area 38.6 ha
Gaussian h = 100 m: peak 9.7 planes/ha; peak crown density 19.7% of the ground under plane crowns
correlation between count and crown-area surfaces: r = 0.859
count peak at E 528438 N 185888; crown-area peak at E 529738 N 183462 (2,751 m apart)

=== GeoTIFF export ===
edge correction factor 1/c(x): median 1.00, max 3.69 (cells on the boundary)
wrote output\camden_london_plane_density.tif: 305 x 267 cells, EPSG:27700, 25 m, float32, nodata -9999, 131 KB
  read back: max 11.0 trees/ha, mean 1.51 trees/ha (the borough average is 1.51)

=== relative risk: London planes vs all other council trees ===
cases 3,292 planes, controls 24,260 other trees; common Gaussian h = 150 m
correlation of the raw plane density with the density of all council trees: r = 0.45
72% of the borough has >= 5 other trees per ha (elsewhere the ratio is masked)
log2 relative risk, 1st to 99th percentile: -3.65 to 2.30 (planes 0.08x to 4.9x their borough-wide share)
pointwise p <= 0.05 (planes over-represented), 199 random labellings: 28.9% of valid cells (4.50 km2); about 5% would be flagged by chance alone

=== plane share by land owner ===
London plane share of council trees by contract area: Highways 17%, Parks 13%, Housing 7%, Education 5%, Corporate Landlord 2%, Valuers 0%
borough-wide share: 11.9%