arXiv:2607.01082v1 [cs.LG] 1 Jul 2026
When Context Compensates for Sparse Event History: AlphaEarth for Spatio-Temporal Point-Process Forecasting Yahya Aalaila1,5 , Mouad Elhamdi2 , Gerrit Großmann1 , Daniel Jenson3 , Elizaveta Semenova4 and Sebastian Vollmer1,5 1 German Research Center for Artificial Intelligence (DFKI) 2 Université Mohammed VI Polytechnique 3 University of Oxford 4 Imperial College London 5 Rhineland-Palatinate Technical University of Kaiserslautern-Landau (RPTU) [email protected] Abstract Spatio-temporal point-process models must often generalise across space when local event histories are sparse. We study whether exogenous spatial context can compensate in such regimes. Using a fixed log-Gaussian Cox process backbone, we compare an event-only model with the same model augmented by AlphaEarth embeddings as linear spatial context. We evaluate spatial transfer on emergency medical services (EMS) forecasting across eight heldout regions, fixed forecast anchors, and a sweep over history length w, using only AlphaEarth (AE) embeddings available strictly before each anchor. AE improves out-of-region predictive performance across all history regimes, with the largest gains under scarce histories: approximately 2–6× multiplicative improvements at 1 − 2 weeks, tapering to roughly 10–20% at w = 20–104 weeks. These results show that contextual information can substantially stabilise spatially transferred point-process forecasts when event history is limited.
1
INTRODUCTION
Spatio-temporal point-process (STPP) models forecast future events by estimating how risk varies over space and time from previously observed event histories. Yet they are often asked to generalize precisely where that history is weakest. Consider an emergency medical services (EMS) agency forecasting next-week call demand in a newly developed tract, a boundary region with limited prior coverage, or a neighborhood whose recent call history is too sparse to reveal a stable risk pattern. A history-driven point-process model may observe only a handful of local events, even though the area already has observable spatial structure: its built environment, land-use pattern, surrounding settlement density, and broader geospatial context. This raises a basic question: when event history is scarce, can external spatial context compensate? STPPs are a natural setting for this question because they forecast future events from observed histories while allowing
Figure 1: Conceptual motivation. In spatial transfer, contextual information can stabilise point-process forecasts when local event history is sparse.
exogenous covariates to shape the conditional intensity [Diggle, 2013; Diggle et al., 2013; Reinhart, 2018]. This exposes an endogenous–exogenous trade-off: event histories reflect where the process has recently concentrated, while contextual information describes the structure of the domain in which those events occur. We lack controlled evidence on whether such context can stabilise spatial transfer when local history is scarce, and how its value changes as more event history becomes available. This trade-off matters because spatial event risk is shaped by persistent structure in the domain—built environment, mobility networks, land cover, infrastructure, and other properties of place—that event histories can only recover indirectly, especially under short observation windows or spatial transfer. Studying the role of such context has historically required bespoke remote-sensing pipelines and hand-engineered spatial features [Claverie et al., 2018]. AlphaEarth (AE) embeddings make the question easier to examine cleanly: they provide standardized, foundation-model geospatial representations that compress multi-source satellite and environmental signals into compact 64-dimensional vectors per location and year [Brown et al., 2025]. We use AE embeddings as a controlled source of exogenous spatial context to test how contextual information complements event
history across history regimes. Figure 1 illustrates this setting. Our goal is not to show that exogenous covariates can help STPPs in general, which is already well established, but to quantify when off-the-shelf foundation-model geospatial embeddings improve spatial transfer relative to accumulating local event history. We begin from a simple intuition: external spatial context should matter most when local event history is scarce, and its incremental value should diminish as the event-only model accumulates enough data to recover stable background structure. We test this intuition in a controlled EMS forecasting study. To avoid conflating contextual information with model capacity, we fix a transparent LGCP backbone and compare two matched models: an event-only LGCP and the same LGCP augmented with AE embeddings as linear spatial context. We evaluate geographically held-out forecasting across eight disjoint spatial masks within Montgomery County, Pennsylvania, under fixed forecast anchors and a sweep over history-window lengths w. AE is treated as strictly exogenous: for each forecast anchor, we use only the latest annual embedding slice available before the anchor and hold it fixed during training and evaluation. The results support the history–context intuition strongly. Across all held-out regions, AE improves out-of-region predictive performance for every history length considered. The gains are largest in sparse-history regimes: with only 1-2 weeks of training data, AE yields approximately 2–6× multiplicative improvements in predictive density relative to the event-only baseline. The advantage narrows as more history accumulates, but remains positive even for 20–104 weeks of training history, where gains persist at roughly 10–20%. Posterior field summaries further indicate that AE accelerates early level correction and produces smoother, more stable spatial structure.
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PROBLEM SETUP
We study LGCPs for spatio-temporal events under varying history-window regimes, with and without exogenous spatial context. The goal is to quantify how history length w and AE embeddings affect spatially held-out predictive performance.
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Models and Training
In an LGCP, the conditional intensity at (t, s) does not explicitly condition on the event history at prediction time; rather, the chosen history window determines which past events enter estimation. The model assumes, ( λ(t, s) = exp η(t, s) , η(t, s) = αβ (t, s) + g(t, s), where g ∼ GP(0, k) captures smooth spatio-temporal variation, and αβ (t, s) collects fixed effects and contextual terms. For computational convenience, we model the spatiotemporal effect as an additive term, g(t, s) = fs (s) + ft (t). This decomposition reduces inference cost while still allowing separate spatial and temporal variation. We also exclude neural components because they add flexibility that can improve fit independently of the added spatial context. By keeping the
model simple, observed performance differences can be attributed to the added spatial context rather than to increased model complexity. In this study, we consider two models: Event-only LGCP.
The intensity is
λE (t, s) = exp{β0 + fs (s) + ft (t)}.
(1)
AE-augmented LGCP. We augment the log-intensity with AE spatial context, λAE (t, s) = exp{β0 + z(t, s)⊤ β + fs (s) + ft (t)}.
(2)
AE vectors z(t, s) ∈ R64 are piecewise-constant in time at an annual cadence: for t ∈ (τy , τy+1 ], z(t, s) = z y (s). For a forecasting anchor ta , we use the last annual slice strictly preceding the anchor and hold it fixed during training and evaluation. Forecasting protocol. We partition S into disjoint regions (m) (m) Rin and Rout for mask m. Estimation uses only events in (m) (m) Rin , while evaluation uses only Rout . Anchor times {ta } are chosen in July 2020 via a back-off heuristic to ensure nonempty windows. In total, we evaluate 5 forecast anchors per mask. For anchor ta , we use the last available annual AE slice with timestamp strictly less than ta and hold it fixed over the forecast horizon. The forecast horizon is [ta , ta + H), with H = 7 days, and the fitting interval is [ta − w, ta ). We sweep w ∈ W = {1, 2, 4, . . . , 104} weeks. For each mask m, anchor ta , and history length w, the (m) fitting data consist of events in Rin × [ta − w, ta ); we denote these events by Dw . Evaluation is performed on the held-out (m) domain DT = Rout × [ta , ta + H), with observed test events YT ⊂ DT . Estimation and inference. We use the PriorVAE reparameterization of the spatial GP prior [Semenova et al., 2022], representing g through a low-dimensional latent variable decoded back to the field. This improves inference tractability for the repeated (w, ta ) sweeps. We fit all models with stochastic variational inference (SVI). For a fitting window, the log-likelihood is Z X L(β, θ, g) = log λ(ti , si )− λ(t, s) ds dt. (m,a)
(m,a)
(ti ,si )∈Yw
Ωw
where Ωw is the spatio–temporal region induced by the history window and forecast setup. All integrals are evaluated by numerical quadrature consistent with the model’s discretization.
2.2
Evaluation
Using the notation above, let Yw denote the fitting events for a given mask m, anchor ta , and history length w. Evaluation is (m) carried out on the held-out test domain DT = Rout × [ta , ta + H), with observed test events YT ⊂ DT . For M ∈ {E, AE}, let pM (· | Yw ) denote the posterior predictive density under the event-only or AE-augmented model.
Held-out ELPD. We evaluate predictive performance using held-out expected log predictive density (ELPD) on DT [Vehtari et al., 2017]: X ELPDM (w; m, a) = log pM (yi | Yw ) yi ∈YT
Z −E
λM (s, t; θ) ds dt Yw .
DT
(3) All integrals use the same numerical quadrature as the fitted model, including time-bin overlaps and polygon–cell area fractions. Paired contrasts and event-level density ratios. All comparisons are paired at the level of (m, a, w), controlling for mask geometry and anchor-specific demand. The primary contrast is ∆(w; m, a) = ELPDAE (w; m, a) − ELPDE (w; m, a). (4) To isolate how much predictive density the AE model assigns to the realized events, we also report the per-event log-density contrast 1 X pAE (yi | Yw ) ∆e (w; m, a) = log . (5) |YT | pE (yi | Yw )
Figure 2: Spatial distribution of EMS 911 calls in Montgomery County, Pennsylvania, from 2017 to 2020.
yi ∈YT
This quantity is measured in natural-log units per event. We additionally report exp{∆e (w; m, a)}, which is the geometricmean multiplicative density ratio assigned to realized held-out events by the AE model relative to the baseline [Gneiting and Raftery, 2007]. For each mask m, we aggregate across anchors using the median. Across masks, we summarize variation using either median and IQR ribbons or mean curves with normalapproximate 95% confidence bands. Because the number of held-out masks is small, these bands should be read as acrossmask variability summaries rather than formal populationlevel confidence intervals. Additional summaries. We also report the paired percent ELPD gain, gain(w; m, a) =
∆(w; m, a) , |ELPDE (w; m, a)|
as a scale-normalized descriptive comparison. To summarize posterior field structure, we track the spatial standard deviation of the posterior mean log-intensity across grid cells, with an analogous temporal summary across time bins. These curves describe how inferred spatial and temporal structure evolves with history length. The event-level density ratio (exp ∆e ) and the percent ELPD gain are complementary but distinct summaries: the former is a geometric-mean predictive-density ratio over realised events, while the latter normalizes the total held-out ELPD difference by the event-only ELPD.
3
EXPERIMENTS AND RESULTS
3.1
Data and AE Embeddings
We use the MontcoAlert 911 Calls dataset, focusing on EMS computer-aided dispatch incidents in Montgomery County,
Pennsylvania, from 2017 to 2020. Each incident is represented as a spatio-temporal event (ti , si ), where si = (xi , yi ) denotes planar coordinates in a metric projected coordinate reference system (CRS). The spatial domain S is defined by the county boundary polygon. Timestamps are converted to UTC, coordinates are reprojected to the metric CRS, and events outside S are removed. All spatial computations are performed in the projected CRS. Figure 2 shows the spatial distribution of the resulting events. Across the evaluated anchors (40 mask–anchor units: 8 masks × 5 anchors), the one-week history windows contain a mean of 1,908 training events in the observed region (IQR 1,793–1,982) and a mean of 262 test events in the held-out region (IQR 179–381). Training event counts increase approximately linearly with w (mean slope ≈ 2,167 events/week; R2 = 0.999), while held-out test counts are fixed by the one-week test horizon. This clarifies that the reported history lengths correspond to genuinely sparse event regimes at small w. Following Sec. 2, we attach 64-dimensional AE embeddings z(t, s) ∈ R64 to locations in S. The embeddings are piecewise constant over annual intervals: for t ∈ (τy , τy+1 ], we set z(t, s) = z y (s). To prevent temporal leakage, for each forecasting anchor ta we select only the latest annual embedding slice strictly preceding the anchor, τy∗ < ta , and use z y∗ (s) throughout both the training window and the forecast horizon. Thus, AE enters the model as static exogenous spatial context available at forecast time.
3.2
Implementation Details
The latent spatial and temporal fields fs and ft in Equations (1) and (2) follow the VAE-based parameterization of Manring et al. [2025]. For both the event-only and AE-augmented
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Figure 3: History–context trade-off across held-out spatial regions. Left: Per-mask paired per-event log-score difference ∆e (w; m) versus history length w. Right: Aggregate trend across masks with normal-approximate uncertainty bands. Values above y = 0 favour the AE-augmented model.
Figure 4: Held-out ELPD curves for two representative spatial masks. Blue: event-only baseline. Orange: AE-augmented model. Black: density ratio exp{∆e (w; m)}, with parity at y = 1. AE gives the largest advantage in sparse-history regimes.
arms, the GP prior is reparameterized with PriorVAE. Spatial quadrature uses a 25 × 25 grid, and time is discretized into nt = 50 uniform bins over [t1 , t2 ). We fit each model with SVI for 4,000 steps at learning rate 10−2 , and draw 1,000 posterior samples from the variational guide for evaluation. Held-out predictive log densities on Rout × [t1 , t2 ) are computed by log-mean-exp aggregation across posterior samples. Temporal integrals use fractional bin overlaps with [t1 , t2 ), while spatial integrals use polygon overlays between the computational grid and Rout with exact area fractions.
3.3
Density ratio
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Figure 3 summarizes how the predictive value of AE changes with the available event-history length w. The left panel shows the paired per-event log-score difference ∆e (w; m) for each held-out spatial mask, aggregated across forecast anchors. The right panel reports the corresponding aggregate trend across masks. Across the entire history range, the curves remain above the parity line, indicating that the AE-augmented model consistently improves out-of-region predictive performance relative to the event-only baseline. The gain is largest in sparse-history regimes and decreases as more events become available. At one to two weeks of training history, AE produces substantial improvements in predictive density, corresponding to roughly 2–6× multiplicative gains over the event-only baseline. The advantage narrows as w increases, but remains positive through long-history regimes, including 20–104 weeks of training data. This pattern supports the central hypothesis of the paper: exogenous spatial context is most valuable when endogenous event evidence is weak, while continuing to complement event history even after substantial data accumulate. Minor non-monotonicity across weeks reflects the fact that longer histories add older events that may be less aligned with a given forecast anchor, producing finite mask-anchor variability around the dominant trend. Figure 4 shows this pattern directly on total held-out ELPD for two representative masks. In both regions, the AEaugmented model achieves higher held-out ELPD than the event-only baseline for every history length. The separation is largest at short histories and narrows as more data are included. The secondary axis reports exp{∆e (w; m)}, the geometricmean predictive-density ratio, which makes the scale of the improvement directly interpretable. Figure 5 summarizes the same effect as a multiplicative
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Figure 5: Mean multiplicative improvement in held-out predictive density versus history length. Bars report exp{∆e (w; m)} averaged across masks, with normal-approximate descriptive intervals. Values above the parity line y = 1 indicate higher predictive density under the AE-augmented model.
predictive-density ratio. Values above one indicate that AE assigns higher predictive density to the realized held-out events than the event-only model. The mean density ratio is 5.42× at one week and 2.37× at two weeks, then decreases while remaining above parity for all selected history lengths. Figure 6 confirms that this effect is not driven by a small subset of masks: the distribution of paired per-event log-score differences remains strictly positive across regions, with the largest gains concentrated in the shortest-history regimes.
3.4
Posterior Field Structure
The predictive gains are accompanied by systematic differences in the fitted latent spatial fields. Figure 7 summarizes two posterior field statistics as the history length w increases. The top row reports µ̄(w), the spatial average of the posterior mean log-intensity over the held-out region. Both models rapidly adjust their overall intensity level as history becomes available and then plateau, but the AE-augmented model converges more quickly in the low-history regime. The bottom row reports SDx (µ; w), the spatial standard deviation of posterior mean log-intensity across the heldout region. The AE-augmented model produces consistently smoother spatial fields than the event-only baseline, while both models develop stronger spatial contrast as more history accumulates. Taken together, these summaries suggest that
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Figure 6: Distribution of paired per-event log-score improvements ∆e (w; m) across masks at selected history lengths. Each point represents the median improvement for one mask across anchors; boxes show the interquartile range and median. Improvements remain above the parity line y = 0 for all selected history lengths, with the largest gains at w ∈ {1, 2} weeks.
AE improves sparse-history forecasting by stabilizing early estimates of the held-out risk surface, while its smaller longhistory gains reflect continued refinement of spatial structure rather than correction of gross level errors.
RELATED WORK
Classical STPPs provide the probabilistic foundation for modeling events in continuous space and time. Frameworks such as IPPs provide interpretable risk maps by linking the logintensity to observed features via likelihood-based inference [González et al., 2016; Moraga, 2023]. LGCPs extend IPPs by imposing a latent Gaussian field over the log-intensity, capturing residual clustering and non-stationarity beyond measured covariates [Møller et al., 1998]. Recent toolchains have improved the scalability and routine use of LGCPs for both point-level and aggregated outcomes [Watson, 2024]. These models are widely used in epidemiology for spatial smoothing and uncertainty quantification [Amaral et al., 2023; Meyer et al., 2017]. In recent years, deep learning has emerged as a powerful paradigm for STPPs, demonstrating superior predictive performance and the ability to capture highly complex dependencies. This line of work includes models based on neural ODEs [Chen et al., 2020] and, more recently, score-based generative models that frame event generation as a diffusiondenoising process [Yuan et al., 2023; Lüdke et al., 2024]. The flexibility of these architectures comes with reduced interpretability and higher computational demands, which can limit adoption in high-stakes settings. Integrating exogenous covariates is key to improving both explanation and prediction. Best practices in spatial statistics advocate a systematic covariate workflow that includes exploratory analysis, mechanistic justification, regularization, and rigorous out-of-sample evaluation [Giorgi et al., 2021]. Within the Cox-process family, covariates generally influence the mean structure of the latent field, which in turn accounts for unobserved heterogeneity [Møller et al., 1998; Watson, 2024]. Toolkits designed for environmental health and epidemiology
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Figure 7: Posterior spatial-field summaries versus history length. Top: spatial mean log-intensity µ̄(w). Bottom: spatial contrast SDx (µ; w). Left: AE-augmented model; right: event-only baseline. Bands summarize across-mask variability.
offer practical approaches for effective integration [Moraga, 2023; Meyer et al., 2017]. On the temporal side, [Meng et al., 2024] proposes an interpretable transformer that explicitly disentangles the influence of event history from covariate representations, enabling attribution of covariate importance without sacrificing predictive accuracy. EMS demand modeling has long treated calls as inhomogeneous Poisson events on fine space–time grids [Zhou et al., 2015; Zhou, 2016]. To address sparsity and periodicity, time-varying Gaussian mixtures fix spatial components while allowing mixture weights to evolve, improving accuracy over operational heuristics [Zhou et al., 2015]. Nonparametric baselines reweight historical incidents by recency and relevance using spatio-temporal kernel–density estimation [Zhou and Matteson, 2015], and kernel warping adapts to complex urban geometry by transporting kernels to a historical point cloud [Zhou and Matteson, 2016]. Because interventions occur on road networks, linear-network STPPs with nonseparable space–time interactions sharpen fit and localization [Gilardi et al., 2024]. Complementary modeling choices capture additional data characteristics: zero-inflated Poisson regression improves calibration under structural zeros [Steins et al., 2019], and self-exciting formulations capture short-term clustering [Li et al., 2019].
5
CONCLUSION
Main finding. This work examined when exogenous spatial context can complement limited event history in spatiotemporal point-process forecasting. Using matched LGCP arms, we isolated the contribution of AlphaEarth embeddings under spatial hold-out evaluation. Across eight heldout regions in Montgomery County, Pennsylvania, the AEaugmented model consistently outperformed the event-only baseline. The gains were largest with short histories, reaching 2 to 6× multiplicative improvements with only one to two weeks of training events, and remained positive with longer histories. This suggests that contextual information can sta-
bilise spatial transfer when local event evidence is weak. The gains are plausibly driven by persistent properties of place that AE embeddings may encode, such as land cover, built form, settlement density, infrastructure, and other remote-sensingderived proxies. We do not interpret individual AE dimensions causally. Instead, AE is treated as a compact external representation of spatial context whose predictive value is evaluated under a controlled spatial-transfer protocol. Implications for STPPs. More broadly, the results suggest that context should be treated as a core modelling component rather than an optional extension. Spatial and temporal domains are increasingly accompanied by structured external information, including remote-sensing embeddings, mobility fields, land-use layers, weather, infrastructure, and other contextual signals. Event histories may recover some of these effects indirectly, but only after enough events have been observed. This motivates more systematic use of contextual information in flexible neural and representation-rich STPPs. Operational relevance. For EMS forecasting, context appears most useful in operationally difficult regimes, such as newly developed areas, boundary regions, or locations with limited recent call history. Better spatial transfer in these settings could support more reliable demand estimation and preparedness. At the same time, probabilistic gains are not deployment value by themselves. Future work should connect these improvements to decision-facing evaluations, including response time, unit availability, and other operational constraints. Limitations and Future Directions. Our evaluation focuses on proper predictive scores—held-out ELPD and per-event log-density contrasts—rather than operational outcomes. A natural next step is to assess decision-centric metrics such as Predictive Accuracy Index, calibration diagnostics, and CRPS, and to connect forecast quality to downstream EMS decisions through simulation-based evaluation. Methodologically, the present study establishes the value of contextual information within a transparent LGCP backbone. The next step is to develop STPP architectures that integrate high-dimensional contextual fields more flexibly, including neural models, while preserving reliable spatial generalisation. In parallel, the field needs importance measures tailored to contextual information in point-process models, so that improved forecasts can also yield sharper understanding of the signals driving spatiotemporal risk.
References André Victor Ribeiro Amaral, Jonatan A González, and Paula Moraga. Spatio-temporal modeling of infectious diseases by integrating compartment and point process models. Stochastic Environmental Research and Risk Assessment, 37(4):1519–1533, 2023. Christopher F Brown, Michal R Kazmierski, Valerie J Pasquarella, William J Rucklidge, Masha Samsikova, Chenhui Zhang, Evan Shelhamer, Estefania Lahera, Olivia Wiles, Simon Ilyushchenko, et al. Alphaearth foundations: An embedding field model for accurate and efficient
global mapping from sparse label data. arXiv preprint arXiv:2507.22291, 2025. Ricky TQ Chen, Brandon Amos, and Maximilian Nickel. Neural spatio-temporal point processes. arXiv preprint arXiv:2011.04583, 2020. Martin Claverie, Junchang Ju, Jeffrey G Masek, Jennifer L Dungan, Eric F Vermote, Jean-Claude Roger, Sergii V Skakun, and Christopher Justice. The harmonized landsat and sentinel-2 surface reflectance data set. Remote sensing of environment, 219:145–161, 2018. Peter J Diggle, Paula Moraga, Barry Rowlingson, and Benjamin M Taylor. Spatial and spatio-temporal log-gaussian cox processes: Extending the geostatistical paradigm. Statistical Science, 28(4), 2013. Peter J Diggle. Statistical analysis of spatial and spatiotemporal point patterns. CRC press, 2013. Andrea Gilardi, Riccardo Borgoni, and Jorge Mateu. A nonseparable first-order spatiotemporal intensity for events on linear networks: An application to ambulance interventions. The Annals of Applied Statistics, 18(1):529–554, 2024. Emanuele Giorgi, Claudio Fronterrè, Peter M Macharia, Victor A Alegana, Robert W Snow, and Peter J Diggle. Model building and assessment of the impact of covariates for disease prevalence mapping in low-resource settings: to explain and to predict. Journal of The Royal Society Interface, 18(179):20210104, 2021. Tilmann Gneiting and Adrian E Raftery. Strictly proper scoring rules, prediction, and estimation. Journal of the American statistical Association, 102(477):359–378, 2007. Jonatan A González, Francisco J Rodrı́guez-Cortés, Ottmar Cronie, and Jorge Mateu. Spatio-temporal point process statistics: a review. Spatial Statistics, 18:505–544, 2016. Chenlong Li, Zhanjie Song, and Xu Wang. Nonparametric method for modeling clustering phenomena in emergency calls under spatial-temporal self-exciting point processes. IEEE Access, 7:24865–24876, 2019. David Lüdke, Enric Rabasseda Raventós, Marcel Kollovieh, and Stephan Günnemann. Unlocking point processes through point set diffusion. arXiv preprint arXiv:2410.22493, 2024. Isaac Manring, Honglang Wang, George Mohler, and Xenia Miscouridou. Bstpp: a python package for bayesian spatiotemporal point processes. Journal of Applied Statistics, pages 1–20, 2025. Zizhuo Meng, Boyu Li, Xuhui Fan, Zhidong Li, Yang Wang, Fang Chen, and Feng Zhou. Transfeat-tpp: An interpretable deep covariate temporal point processes. arXiv preprint arXiv:2407.16161, 2024. Sebastian Meyer, Leonhard Held, and Michael Höhle. Spatiotemporal analysis of epidemic phenomena using the r package surveillance. Journal of Statistical Software, 77:1–55, 2017. Jesper Møller, Anne Randi Syversveen, and Rasmus Plenge Waagepetersen. Log gaussian cox processes. Scandinavian journal of statistics, 25(3):451–482, 1998.
Paula Moraga. Spatial statistics for data science: theory and practice with R. Chapman and Hall/CRC, 2023. Alex Reinhart. A review of self-exciting spatio-temporal point processes and their applications. Statistical Science, 33(3):299–318, 2018. Elizaveta Semenova, Yidan Xu, Adam Howes, Theo Rashid, Samir Bhatt, Swapnil Mishra, and Seth Flaxman. Priorvae: encoding spatial priors with variational autoencoders for small-area estimation. Journal of the Royal Society Interface, 19(191):20220094, 2022. Krisjanis Steins, Niki Matinrad, and Tobias Andersson Granberg. Forecasting the demand for emergency medical services. In the 52nd Hawaii International Conference on System Sciences, 2019, January 8-11, Grand Wailea, Maui, Hawai’i, pages 1855–1864. University of Hawai’i at Manoa, 2019. Aki Vehtari, Andrew Gelman, and Jonah Gabry. Practical bayesian model evaluation using leave-one-out crossvalidation and waic. Statistics and computing, 27(5):1413– 1432, 2017. Samuel I Watson. Twenty ways to estimate the log gaussian cox process model with point and aggregated case data: the rts2 package for r. arXiv preprint arXiv:2403.09448, 2024. Yuan Yuan, Jingtao Ding, Chenyang Shao, Depeng Jin, and Yong Li. Spatio-temporal diffusion point processes. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 3173–3184, 2023. Zhengyi Zhou and David S Matteson. Predicting ambulance demand: A spatio-temporal kernel approach. In Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, pages 2297–2303, 2015. Zhengyi Zhou and David S Matteson. Predicting melbourne ambulance demand using kernel warping. The Annals of Applied Statistics, pages 1977–1996, 2016. Zhengyi Zhou, David S Matteson, Dawn B Woodard, Shane G Henderson, and Athanasios C Micheas. A spatio-temporal point process model for ambulance demand. Journal of the American Statistical Association, 110(509):6–15, 2015. Zhengyi Zhou. Predicting ambulance demand: challenges and methods. arXiv preprint arXiv:1606.05363, 2016.