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REVIEW 1 major objections 5 minor 93 references

ROC Curves for Spatial Point Patterns and Presence-Absence Data

T0 review · 1 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read For spatial presence-absence and point-pattern data, the ROC curve measures ranking ability within a fixed study region — not goodness-of-fit — and AUC is exactly a rescaled test of the hypothesis that covariates have no effect.

desk verdict A clear, careful reframing of ROC/AUC for spatial data that will change how applied ecologists and geologists read AUC values; the abstract overstates the hypothesis-test connection, but the core negative result holds. read the letter →

arxiv 2506.03414 v1 pith:WQOQLSIS submitted 2025-06-03 stat.ME

Adrian Baddeley , Ege Rubak , Suman Rakshit , Gopalan Nair This is my paper
classification stat.ME MSC 62M3062G1062-08
keywords ROCcurvesAUCspatialpointpatternspresence-absencedataspeciesdistributionmodelsmineralprospectivityrankingabilityBerman-Waller-Lawsontest
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper challenges a widespread practice: using the ROC curve and its area (AUC) to 'validate' spatial models such as species distribution models and mineral prospectivity maps. It argues that ROC does not measure goodness-of-fit and only weakly measures predictive power; it measures ranking ability — how well a covariate or model score sorts a fixed study region into high- and low-density parts. Because that ranking is tied to the size, shape, and inhomogeneity of the region, an AUC value cannot be extrapolated to new regions, to sub-regions, or to scenarios with changed covariates, such as climate change. The argument is made precise by exact identities linking AUC to classical tests of 'no covariate effect', and by new ROC variants (covariate ROC, baseline-adjusted and partial ROC) that give the curve a legitimate diagnostic use. If the paper is right, published AUC claims for spatial models need to be re-read as statements about the covariates, not about the models.

What carries the argument

The load-bearing objects are two curves and four identities. The covariate ROC (C-ROC) thresholds a spatial covariate and plots the fraction of observed points above threshold against the fraction of region area above threshold, with no model involved; the model ROC (M-ROC) does the same using fitted presence probabilities or fitted intensity as the score. The argument runs on: monotone invariance of the M-ROC (Lemma 6); collapse of the M-ROC to the C-ROC for any monotone single-covariate model (Lemma 7); the exact identity linking AUC to Berman's second no-effect test statistic, $V_2 = \sqrt{12n}(\mathrm{AUC} - 1/2)$ (Lemma 10); and the derivative identity $dR/dp = \rho(F_P^{-1}(p))/\kappa$, which expresses the ROC slope as the resource-selection function $\rho$ (the intensity as a function of the covariate) divided by mean intensity (Proposition 1). This last identity is what makes the curve's shape diagnostic: it implies the model-predicted M-ROC is always concave, so a non-concave empirical curve signals that a monotone model is inappropriate, and it identifies $\rho$ — not the ROC — as the object that can legitimately be extrapolated between regions.

What would settle it

Simulate many realisations of a clustered point process (for instance a Thomas or Neyman-Scott process) whose intensity depends on a single covariate, and, for comparison, a Poisson process with the same marginal intensity function. Compute the empirical C-ROC, its AUC, and Berman's second no-effect test statistic $V_2$ in both settings. If $V_2 = \sqrt{12n}(\mathrm{AUC} - 1/2)$ and the plug-in variance $\hat\sigma^2(p) = R(p)(1-R(p))/n$ still track the observed Monte Carlo spread for the clustered process, the paper's bridge from AUC to the no-effect hypothesis survives dependence; if not, the ranking interpretation of AUC holds exactly only under Poisson-type independence, and dependent spatial data need a new correction.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the model-based ROC curve (M-ROC) used in applied work is very nearly model-free. For a model that depends monotonically on a single covariate, the M-ROC is identical to the covariate-based ROC (C-ROC) computed without any model (Lemma 7); the M-ROC is invariant under any strictly increasing transformation of the predicted probabilities or intensities (Lemma 6); and the AUC equals an exact rescaling of Berman's second test statistic for the null hypothesis that the covariate has no effect, $V_2 = \sqrt{12n}(\mathrm{AUC} - 1/2)$ (Lemma 10). Therefore a high AUC is evidence against the null model of uniform presence probability — it quantifies how strongly the covariate separates the region — not evidence for the correctness of the fitted model. The same identities imply that AUC is a measure of the magnitude of a covariate effect within one specific region, and that different summary tools (ROC, the continuous Boyce index, resource selection functions) used together cannot be treated as independent confirmation of a model, since they are transformations of the same comparison.

Load-bearing premise

The load-bearing premise is that the point pattern is a realisation of a Poisson process — or, for pixel data, that the presence indicators are independent — because the exact identities connecting AUC to the no-effect test statistics and the variance formula $\sigma^2(p)=R(p)(1-R(p))/n$ are derived under that assumption; for clustered or otherwise dependent spatial data the paper proves no analogue.

Editorial extensions

If this is right

  • AUC values reported for species distribution models or mineral prospectivity maps cannot be cited as evidence that the fitted model is appropriate; at most they quantify how well the input covariate separates high- and low-density parts of the specific survey region.
  • ROC and AUC cannot support extrapolation: moving to a new region, restricting to a sub-region (which can trigger Simpson's paradox), or changing covariate values (climate-change scenarios) can change the curve.
  • For any model depending monotonically on a single covariate, the model-based ROC is identical to the covariate-based ROC, so ROC cannot be used to choose between, or even distinguish, such models.
  • Genuine model checking is still possible, but differently: by comparing empirical and model-predicted ROC curves (C-ROC or M-ROC), and by using the fact that a model-predicted M-ROC is always concave, so a non-concave empirical curve signals misspecification.
  • ROC computed from presence-absence data at different pixel sizes is asymptotically consistent as pixel size shrinks to zero, because the limit is the point-pattern ROC computed from exact coordinates.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the paper is right, variable-selection procedures that rank covariates by AUC are quietly selecting for covariates with strongly patchy spatial distributions within the training region; two covariates with the same true ecological or geological effect could receive very different AUCs purely because of how their values are arranged across the map.
  • Because AUC is a rescaled no-effect test statistic, it could in principle be inverted to compute the number of points or survey effort needed to detect a covariate effect of a given size — a power-calculation use the paper does not develop.
  • The region-dependence result suggests that the continuous Boyce index and other ranking metrics used in habitat modelling inherit the same limitation; the transferable object between regions is the resource-selection function itself, not any area-under-curve summary.
  • For clustered point processes, an effective-sample-size correction (analogous to Clifford-Richardson corrections for spatially correlated data) might restore the variance formula $\sigma^2(p)=R(p)(1-R(p))/n$ and the AUC-test equivalence; whether such corrections exist for clustered patterns is a direct testable extension of the paper's variance and hypothesis-test sections.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 5 minor

Summary. The paper clarifies the interpretation of ROC curves and the area under the curve (AUC) when used to evaluate models for spatial presence-absence and point-pattern data. It argues that the customary “model ROC” (M-ROC) does not measure goodness-of-fit of the fitted spatial model, that its interpretation as a measure of predictive ability is weak, and that it is better viewed as a measure of ranking ability within the study region. The authors introduce a covariate-based ROC (C-ROC), establish connections between AUC and the Berman–Waller–Lawson test and between the Youden index and the Kolmogorov–Smirnov test, and develop several extensions (baseline-adjusted ROC, weighted ROC, partial ROC, ROC restricted to subregions, and model-checking by comparing empirical and model-predicted ROC curves). The claims are supported by elementary proofs (Lemmas 1–11, Proposition 1), synthetic examples illustrating Simpson’s paradox and region-dependence, and several real datasets (Beilschmiedia trees, Murchison gold, gastric mucosa, New Brunswick fires, Chorley-Ribble cancer). Open-source R code in spatstat is provided.

Significance. If the conclusions hold, they correct a widespread misinterpretation of published AUC values in species distribution modelling and mineral prospectivity: high AUC should not be read as evidence that a fitted model is appropriate. The paper’s central negative claim is rigorously established: the M-ROC is invariant under monotone transformations of the fitted scores (Lemma 6), collapses to the C-ROC in the single-covariate case (Lemma 7), and is not a goodness-of-fit measure (Section 5.4.3). The paper also contributes new methodology (C-ROC, partial ROC, baseline-adjusted ROC, model-checking diagnostics) and is careful to state its assumptions and limitations, including explicit acknowledgement that the presence-absence variance formula is not formally proven and that the M-AUC extension of the hypothesis-test connection is not derived. The proofs are elementary and correct, and the open-source implementation strengthens reproducibility.

major comments (1)
  1. [Abstract and Section 6.6] The abstract states without qualification that “the area under the ROC curve (AUC) is related to hypothesis tests of the null hypothesis that the explanatory variables have no effect.” The rigorous result, Lemma 10 in Section 6.2.2, is established only for the covariate-ROC (C-ROC) with a single fixed covariate, under the assumption that the point pattern is Poisson (or that pixel indicators are independent). Section 6.6 explicitly concedes that extending the connection to the model-ROC (M-AUC) is “technically complicated” and will depend on the model and fitting algorithm, and gives no asymptotic or bootstrap result for the multi-covariate case that dominates applications. The abstract should therefore be qualified, for example by saying “for the covariate-ROC” or “in the single-covariate case,” or by explicitly stating that the rigorous connection is proven only for the C-ROC. This does not undermine the central negative finding (that AUC is not a goodness-of-fit measure), but it prevents readers from over-inferring the scope of the hypothesis-test connection.
minor comments (5)
  1. [Section 4.3.1] The variance formula (26) for presence-absence data is stated as “expected to be the large-sample asymptotic variances, but a formal proof of this is outside of the scope of this manuscript.” Since this is used later (e.g., in Figure 15) and is a load-bearing tool for confidence bands, I suggest adding a brief remark in Section 10.2.1 (future research) that a rigorous derivation for spatially dependent presence-absence indicators would be valuable.
  2. [Section 6.2.1] In equations (40)–(41), the mean and variance of S are given under the Poisson assumption unconditionally, using λ. It would be clearer to state explicitly that these are the unconditional moments under H0 and that the test can also be carried out conditionally on n, in which case the moments are n times the moments of F0. This would help readers connect (42) to the conditional version of Berman’s second test.
  3. [Section 4.4.3] The statement following Lemma 5 that the C-ROC “is insensitive to extremes, and to small sub-populations” is supported only by the appendix example (Chorley-Ribble). I suggest either citing the appendix explicitly at this point or softening the wording, since the claim is empirical rather than a proven property.
  4. [Lemma 10] The notation AUC< and AUC> is used in equation (43) but AUC> is not defined locally; it is the area under the ordinary (non-reversed) ROC curve. Please define these symbols at their first use to avoid ambiguity.
  5. [Throughout] There are minor typographical issues: in the abstract, “Open sourceRcode” should read “Open source R code”; in Section 3.4, “The covariate information consists” should be “consist”; in Lemma 1’s proof, the phrase “because h is 1–1” would be clearer as “because h is one-to-one.” These do not affect the mathematics.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the core ROC theorems follow directly from definitions and external results; the abstract's M-AUC scope overclaim is a stated limitation, not a circular derivation.

full rationale

The derivation chain is self-contained. Lemma 6 (invariance of the M-ROC under strictly increasing transformations of fitted probabilities) and Lemma 7 (collapse of the M-ROC to the C-ROC for a single covariate) are immediate set-theoretic consequences of the threshold definitions in (31), (18), (22) and (23); they do not assume the goodness-of-fit conclusion. Lemma 10 relating the C-AUC to Berman's second test statistic is obtained by applying the probability integral transform to the empirical C-ROC and using Fubini's theorem; Berman's test is cited to an external, non-self source (Berman 1986). Proposition 1 connecting the ROC slope to the resource selection function follows by differentiating the point-process intensity relationship (49) and the definitions of TP and FP. Lemma 9's claim that the theoretical M-ROC dominates the C-ROC uses the Neyman-Pearson lemma as an external theorem. None of these steps fits a parameter to data and then renames that fit as a prediction. The model-predicted M-ROC of Section 5.1.1 is explicitly described as another estimator of the theoretical M-ROC, and Section 9 states that 'Perfect agreement between R_hat-lambda,x(p) and R_hat-lambda,hat-lambda(p) does not prove the model is correct,' which disclaims any validation claim that could be circular. The paper also flags its own limitations: Section 6.6 concedes that extending the C-ROC/Berman connection to the data-dependent M-AUC is 'technically complicated' and will depend on 'the model and the fitting algorithm'; Section 4.3.1 says a formal proof of the presence-absence variance is 'outside of the scope of this manuscript'; and Appendix D documents a case where ROC/AUC fail to detect an effect affecting only a small subpopulation. These are coverage and correctness caveats, not circularity. Self-citations to spatstat and to the authors' earlier estimators support software and auxiliary methods, but the central interpretive claims are proven from definitions, standard point-process identities, and external results. No circular step can be exhibited from the paper's own equations.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central results are deterministic identities derived from the definitions of ROC curves and spatial point processes. No free parameters are fitted to derive the main theorems. The examples use fitted models only for illustration. The enumerated assumptions are standard distributional and regularity conditions, stated explicitly in the text.

assumptions (4)
  • domain assumption The point process X is Poisson, or conditionally on the total count the point locations are i.i.d.
    Used to derive the binomial variance (25)-(26) and to connect AUC to Berman's tests in Section 6.2. The paper notes this in Section 4.3.1.
  • domain assumption For presence-absence data, the indicators y_j for different pixels are independent.
    Stated as an assumption for the large-sample variance of the C-ROC in Section 4.3.1; the paper does not provide a formal proof.
  • domain assumption The covariate Z is differentiable with nonzero gradient, ensuring FP is differentiable.
    Invoked in Proposition 1 for the slope formula (50); a sufficient condition is cited in Section 7.2.
  • domain assumption The fitted model is correctly specified for the model-predicted ROC to be a consistent estimator of the theoretical ROC.
    Stated in Sections 5.1.1 and 9.1 for the curve-comparison diagnostics.

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Cite this review

Pith. "Pith review of ROC Curves for Spatial Point Patterns and Presence-Absence Data." pith.science (2026). https://pith.science/paper/WQOQLSIS

@misc{pith2026250603414,
  author       = {Pith},
  title        = {Pith review of: ROC Curves for Spatial Point Patterns and Presence-Absence Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WQOQLSIS}},
  note         = {Machine review of arXiv:2506.03414}
}
read the original abstract

Receiver Operating Characteristic (ROC) curves have recently been used to evaluate the performance of models for spatial presence-absence or presence-only data. Applications include species distribution modelling and mineral prospectivity analysis. We clarify the interpretation of the ROC curve in this context. Contrary to statements in the literature, ROC does not measure goodness-of-fit of a spatial model, and its interpretation as a measure of predictive ability is weak; it is a measure of ranking ability, insensitive to the precise form of the model. To gain insight we draw connections between ROC and existing statistical techniques for spatial point pattern data. The area under the ROC curve (AUC) is related to hypothesis tests of the null hypothesis that the explanatory variables have no effect. The shape of the ROC curve has a diagnostic interpretation. This suggests several new techniques, which extend the scope of application of ROC curves for spatial data, to support variable selection and model selection, analysis of segregation between different types of points, adjustment for a baseline, and analysis of spatial case-control data. The new techniques are illustrated with several real example datasets. Open source R code implementing the techniques is available in the development version of our package spatstat [Baddeley and Turner, 2005, Baddeley et al., 2015] and will be included in the next public release.

Figures

Figures reproduced from arXiv: 2506.03414 by the authors.

Figure 1
Figure 1. Beilschmiedia tree data. Left: Exact tree locations (+) in a 1000 by 500 metre survey region. Right: Presence￾absence indicators for a grid of 10-metre square pixels. Black indicates presence. 3.2 Presence-only and presence-absence data In “presence-only” and “presence-absence” data [Franklin, 2009] the study region is subdivided into cells. In each cell, individuals may be either “present” (observed to be present i… view at source ↗
Figure 2
Figure 2. Gastric mucosa data, showing locations of enterochromaffin-like cells ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Contours of terrain elevation in metres ( [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (29 more)
Figure 4
Figure 4. Figure 4: Murchison data. Left: gold deposits (+), geological faults (—) and greenstone outcrop (grey shading) in a survey region 330 by 400 kilometres across. Vector (spatial coordinate) data, rounded to the nearest metre. Right: Contours of distance (in km) to the nearest geol…
Figure 5
Figure 5. Figure 5: Left and middle: Empirical C-ROC curves computed for the Beilschmiedia data using the presence-absence indicators in 10-metre pixels treating higher values of the covariate as favorable to trees where the covariate is either terrain elevation (Left) or terrain slope (M…
Figure 6
Figure 6. Figure 6: Analysis of gastric mucosa data of Figure 2 using the vertical coordinate [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Left: C-ROC curve (calculated by raw method) for the Murchison gold data and the distance-to-nearest￾fault covariate (solid lines) and pointwise approximate 95% confidence bands (grey shading) calculated using the plug-in estimate of (26). Right: width of confidence ba…
Figure 8
Figure 8. Figure 8: Kernel smoothing estimate (solid line) and pointwise [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Effect of restriction to a subregion. C-ROC curves for the distance-to-nearest fault covariate in the Murchi [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Synthetic example illustrating Simpson’s Paradox for ROC. [PITH_FULL_IMAGE:figures/full_fig_p017_10.png]
Figure 11
Figure 11. Figure 11: Demonstration of Simpson’s Paradox for the data in Figure 10. ROC curves for the [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: M-ROC curves for the logistic regression model of [PITH_FULL_IMAGE:figures/full_fig_p020_12.png]
Figure 13
Figure 13. Figure 13: M-ROC curves for the logistic regression model of [PITH_FULL_IMAGE:figures/full_fig_p020_13.png]
Figure 14
Figure 14. Figure 14: M-ROC curves for Poisson point process models for the Murchison gold deposits in which the intensity [PITH_FULL_IMAGE:figures/full_fig_p020_14.png]
Figure 15
Figure 15. Figure 15: Left: M-ROC curve for the Poisson point process model fitted to the Murchison gold data assuming intensity is a loglinear function of distance-to-nearest-fault. Solid lines: M-ROC curve, raw estimate (leave-one-out). Grey shading: pointwise 95% confidence bands calcul…
Figure 16
Figure 16. Figure 16: Insensitivity of C-ROC to other covariates. [PITH_FULL_IMAGE:figures/full_fig_p026_16.png]
Figure 17
Figure 17. Figure 17: Left: Estimates of the function ρ(d) expressing the intensity of gold deposits as a function of distance to the nearest fault in the Murchison data. Right: corresponding C-ROC curves, computed from left panel using Proposition 1 equation (52). Thick solid lines: kerne…
Figure 18
Figure 18. Figure 18: Estimates of the function ρ(d) expressing the intensity of Beilschmiedia trees as a function of terrain elevation (Left) or as a function of terrain slope (Right). Solid lines: kernel smoothing estimate [Baddeley et al., 2012]. Grey shading: pointwise 95% confidence i…
Figure 19
Figure 19. Figure 19: Empirical C-ROC curves R < Z,x (p) for subsets of the Murchison survey. Black: entire region; red: outside greenstone outcrop; green: inside greenstone outcrop. Covariate is distance to nearest fault, with small distances interpreted as more favorable to gold. cost or…
Figure 20
Figure 20. Figure 20: Analysis of gastric mucosa data of Figure 2 using baseline-adjusted C-ROC. [PITH_FULL_IMAGE:figures/full_fig_p033_20.png]
Figure 21
Figure 21. Figure 21: Partial ROC curves for dropping covariates from a fitted model. Poisson point process, additive loglinear [PITH_FULL_IMAGE:figures/full_fig_p034_21.png]
Figure 22
Figure 22. Figure 22: Partial ROC curves for adding covariates to a fitted model. Poisson point process, additive loglinear [PITH_FULL_IMAGE:figures/full_fig_p034_22.png]
Figure 23
Figure 23. Figure 23: Diagnostics using C-ROC. Model fitted to the Murchison data in which log intensity is an additive linear [PITH_FULL_IMAGE:figures/full_fig_p036_23.png]
Figure 24
Figure 24. Figure 24: Empirical M-ROC curve Rλ, b x (p) (solid lines) and model-predicted M-ROC curve Rλ, b λb(p) (dashed lines) for the Poisson model of the Murchison gold deposits, in which log intensity is a linear function of distance to nearest fault and greenstone indicator. These di…
Figure 25
Figure 25. Figure 25: Models in which the Beilschmiedia presence probability depends on terrain elevation and/or slope. Left column shows contours of fitted probability of presence, p, within each 10-metre pixel, for logistic regression models. Right column shows contours of fitted point p…
Figure 26
Figure 26. Figure 26: New Brunswick fires. Left: fire locations (open circles) and New Brunswick provincial boundary classified into coastline (thin lines) and boundary shared with other territories (thick lines). Right: contour plot of kernel￾smoothed average size of fires. 0.0 0.2 0.4 0.…
Figure 27
Figure 27. Figure 27: Unweighted and weighted ROC curves for the New Brunswick fire locations against distance to the [PITH_FULL_IMAGE:figures/full_fig_p046_27.png]
Figure 28
Figure 28. Figure 28: Chorley-Ribble data. Spatial locations of cases of cancer of the larynx ( [PITH_FULL_IMAGE:figures/full_fig_p047_28.png]
Figure 29
Figure 29. Figure 29: Analysis of the effect of distance to incinerator for the Chorley-Ribble data. [PITH_FULL_IMAGE:figures/full_fig_p048_29.png]
Figure 30
Figure 30. Figure 30: Synthetic example illustrating dependence on study region. [PITH_FULL_IMAGE:figures/full_fig_p049_30.png]
Figure 31
Figure 31. Figure 31: Left: empirical C-ROC curve for the simulated point pattern in the bottom panel of [PITH_FULL_IMAGE:figures/full_fig_p049_31.png]
Figure 32
Figure 32. Figure 32: C-ROC curves for the synthetic example in Figure 30 restricted to different sub-regions. [PITH_FULL_IMAGE:figures/full_fig_p050_32.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.