Research archive.
Earlier spatial, dependence, and contrast experiments. Return to the current three-model workflow.
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Follow the calculation.
Use a CELL ID or open a cell from Map. Follow its real inputs through the fitted models, then test the sensitivity of the result.
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Changing coordinates should not change Mahalanobis distance
Five annual values have four linearly independent temporal contrasts. Subtracting 2021 and taking consecutive differences are invertible representations of the same information—not different observations.
z = C y · Cov(z) = C Cov(y) Cᵀ
Independent equal-variance annual errors: Cov(z) = σ²(I + 11ᵀ). Shared-baseline correlation = 0.5.
This 0.5 is a mathematical example, not an estimated correlation of your forest. Adjacent differences share errors too: their neighbouring error correlation is −0.5 under the same assumptions.
Σλ = (1−λ)S + λT · T = K ⊗ (C Rρ Cᵀ)
z′ = Az, Σ′λ = AΣλAᵀ ⇒ z′ᵀΣ′λ⁻¹z′ = zᵀΣλ⁻¹z
The training mean must also transform. The old diagonal shrinkage target does not generally transform this way. Our new target does. K contains training-only index scales; Rρ is a working AR(1) shape, not a fitted claim about temporal dependence.
The map averages all three λ values within the new Mahalanobis family, then combines it equally with the original anchor-based IF and PCA. The λ menu only changes the displayed cell calculation. Only Mahalanobis is basis-invariant; the complete ensemble is not. These experiments do not replace saved candidate lists.
Numerical tests & protocol · JSON · Read the methods overview
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Inputs → robust standardization
Each feature is a July annual value minus 2021. The actual training fold supplies the median and MAD. Scale = max(1.4826 × MAD, 0.00001). The constant does not assert normality.
Variant ranks → family means → fusion
Family means and their final average are scores, not calibrated percentiles or damage probabilities. Model families are correlated. No chi-square, Gaussian-tail or independent-vote probability is assumed.
These selections load registered, precomputed model refits. Changing fusion recalculates the displayed score only; it does not retrain models or change the saved shortlist.
Registered comparison across the project
The conservative tier is an operational screen, not a significance map: a saved v4 candidate must pass at least 8 of 9 spatial designs, at least 4 of 5 year-deletion ML screens, and retain a negative NDRE slope in all 5 year deletions. Unsupported scenarios do not count as positive votes. Failure means sensitivity or insufficient support, not confirmed healthy forest.
What changes when neighbouring cells travel together?
95% percentile resampling intervals from 2,000 draws, conditional on the observed five-year slope surface. They do not include temporal or measurement uncertainty, and are not forecasts or proof that blocks are independent. Both registered block origins are shown.
Measured spatial structure and model dependence
Moran's I uses a symmetric eight-neighbour graph. The distance curve describes observed structure, not a fitted residual-correlation range. No IID permutation significance test is presented.
A known-null experiment
Simulated Gaussian data with zero true trend, 400 cells and 5 years. The oracle knows the generating covariance; it is not fitted PARTS or HSGP. These rejection rates are not the error rate of the forest screening model.
Articles & methods
Read the methods overview- Ives et al. (2021)Statistical inference for trends in spatiotemporal data
PARTS-inspired temporal GLS and spatial covariance.
Partition combination with cross-partition covariance.
- Lewińska et al. (2023)Beyond “greening” and “browning”: Trends in grassland ground cover fractions across Eurasia that account for spatial and temporal autocorrelation
Ground-cover unmixing and log-ratios; design reference for joint spectral interpretation. Unmixing is not applied here.
- Stoy et al. (2026)Reinterpreting terrestrial ‘warming holes’ in the context of the near-surface atmospheric energy balance
AR(1) and spatial HSGP slopes; dependence-model reference. HSGP is not fitted here.
- DiCiccio & Efron (1996)Bootstrap confidence intervals
Studentized bootstrap confidence intervals.
- Chatterjee, Lahiri & Li (2008)Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models
Parametric bootstrap with nuisance refitting; theoretical reference, not a coverage guarantee for this pipeline.
The methods overview explains the current workflow and its interpretation. The references below provide the published foundations.