Spatio-temporal Point Process Research Articles

Summary statistics for spatio-temporal point processes on linear networks

We propose novel second/higher-order summary statistics for inhomogeneous spatio-temporal point processes when the spatial locations are limited to a linear network. More specifically, letting the spatial distance between events be measured by a regular distance metric, appropriate forms of K- and J-functions are introduced, and their theoretical relationships are studied. The theoretical forms of our proposed summary statistics are investigated under homogeneity, Poissonness, and independent thinning. Moreover, non-parametric estimators are derived, facilitating the use of our proposed summary statistics to study the spatio-temporal dependence between events. Through simulation studies, we demonstrate that our proposed J-function effectively identifies spatio-temporal clustering, inhibition, and randomness. Finally, we examine spatio-temporal dependencies for street crimes in Valencia, Spain, and traffic accidents in New York, USA.

Spatio-Temporal Marked Point Process Model to Understand Forest Fires in the Mediterranean Basin

AbstractUnderstanding and predicting forest fires have proved a highly difficult endeavour, which requires extending and adapting complex models used in different fields. Here, we apply a marked point process approach, commonly used in ecology, which uses multiple Gaussian random fields to represent dynamics of Mediterranean forest fires in a spatio-temporal distribution model. Inference is carried out using Integrated Nested Laplace Approximation (INLA) with , an accessible and computationally efficient approach for Bayesian hierarchical modelling, which is not yet widely used in species distribution models. Using the marked point process approach, intensity of forest fires and dispersion were predicted using socioeconomic factors and environmental and fire-related variables. This demonstrates the advantage of complex model components in accounting for spatio-temporal dynamics that are not explained by environmental variables. Introduction of spatio-temporal marked point process can provide a more realistic perspective of a system, which is of particular importance for a practical and impact-focused worldwide problem such as forest fires.Supplementary materials accompanying this paper appear online.

Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

AbstractIn this paper, we harness a result in point process theory, specifically the expectation of the weighted K-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an estimation method to derive parameter estimates for a particular model assumed for the data. The underlying motivation is to avoid the difficulties associated with dealing with complex likelihoods in point process models and their maximization. The exploited result makes our method theoretically applicable to any model specification. In this paper, we restrict our study to Poisson models, whose likelihood represents the base for many more complex point process models. In this context, our proposed method can estimate the vector of local parameters that correspond to the points within the analyzed point pattern without introducing any additional complexity compared to the global estimation. We illustrate the method through simulation studies for both purely spatial and spatio-temporal point processes and show complex scenarios based on the Poisson model through the analysis of two real datasets concerning environmental problems.

Severe convective storms’ reproduction: empirical analysis from the marked self-exciting point processes point of view

AbstractThe paper focuses on the evaluation of hailstorms’ and thunderstorms winds’ events in the United States of America, in the period from 1996 to 2022, under the marked spatio-temporal self-exciting point processes point of view. The aim of the present article is the assessment and description of the spatio-temporal spontaneous and reproducing activity of severe hailstorms’ and thunderstorms winds’ processes. The present application shows how the spatio-temporal pattern is well-fitted and clearly explainable, according to the flexible semi-parametric ETAS model fitting.

Stelfi: An R package for fitting Hawkes and log-Gaussian Cox point process models.

Modelling spatial and temporal patterns in ecology is imperative to understand the complex processes inherent in ecological phenomena. Log-Gaussian Cox processes are a popular choice among ecologists to describe the spatiotemporal distribution of point-referenced data. In addition, point pattern models where events instigate others nearby (i.e., self-exciting behaviour) are becoming increasingly popular to infer the contagious nature of events (e.g., animal sightings). While there are existing R packages that facilitate fitting spatiotemporal point processes and, separately, self-exciting models, none incorporate both. We present an R package, stelfi, that fits spatiotemporal self-exciting and log-Gaussian Cox process models using Template Model Builder through a range of custom-written C++ templates. We illustrate the use of stelfi's functions fitting models to Sasquatch (bigfoot) sightings data within the USA. The structure of these data is typical of many seen in ecology studies. We show, from a temporal Hawkes process to a spatiotemporal self-exciting model, how the models offered by the package enable additional insights into the temporal and spatial progression of point pattern data. We present extensions to these well-known models that include spatiotemporal self-excitation and joint likelihood models, which are better suited to capture the complex mechanisms inherent in many ecological data. The package stelfi offers user-friendly functionality, is open source, and is available from CRAN. It offers the implementation of complex spatiotemporal point process models in R for applications even beyond the field of ecology.

A Bayesian Inference Method for a Large Magnitude Event in a Spatiotemporal Marked Point Process Representing Seismic Activity

A Bayesian Inference Method for a Large Magnitude Event in a Spatiotemporal Marked Point Process Representing Seismic Activity

Authors’ reply to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

Authors’ reply to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

A spatio-temporal analysis of fire occurrence patterns in the Brazilian Amazon

Wildfires in the Amazon significantly impact the forest structure and carbon cycle. Understanding the patterns of fire occurrence is crucial for effective management. A novel spatio-temporal point process framework was used to analyze changes in fire occurrence patterns in the Brazilian Amazon. A dynamic representation of a Log Gaussian Cox process was used to model the intensity function, which was decomposed into trend, seasonality, cycles, covariates, and spatial effects. The results show a marked decrease in long-term fire occurrence movements between the start of the sample and 2012, followed by an increase until the end of the sample, attributed to governance measures and market mechanisms. Spatial variability of fire occurrence rates in the Brazilian Amazon was successfully captured, with regions having more dry seasons experiencing higher fire occurrence rates. This analysis provides valuable insights into fire occurrence patterns in the Amazon region and the factors driving them.

A neural encoder for earthquake rate forecasting

Forecasting the timing of earthquakes is a long-standing challenge. Moreover, it is still debated how to formulate this problem in a useful manner, or to compare the predictive power of different models. Here, we develop a versatile neural encoder of earthquake catalogs, and apply it to the fundamental problem of earthquake rate prediction, in the spatio-temporal point process framework. The epidemic type aftershock sequence model (ETAS) effectively learns a small number of parameters to constrain the assumed functional forms for the space and time correlations of earthquake sequences (e.g., Omori-Utsu law). Here we introduce learned spatial and temporal embeddings for point process earthquake forecasting models that capture complex correlation structures. We demonstrate the generality of this neural representation as compared with ETAS model using train-test data splits and how it enables the incorporation additional geophysical information. In rate prediction tasks, the generalized model shows >4% improvement in information gain per earthquake and the simultaneous learning of anisotropic spatial structures analogous to fault traces. The trained network can be also used to perform short-term prediction tasks, showing similar improvement while providing a 1000-fold reduction in run-time.

Proposer of the vote of thanks to Narayanan, Kosmidis and Dellaportas and contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

Proposer of the vote of thanks to Narayanan, Kosmidis and Dellaportas and contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

Seconder of the vote of thanks to Narayanan, Kosmidis, and Dellaportas and contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

Seconder of the vote of thanks to Narayanan, Kosmidis, and Dellaportas and contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

Ron Yurko and Rebecca Nugent’s contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’ by Narayanan, Kosmidis, and Dellaportas

Ron Yurko and Rebecca Nugent’s contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’ by Narayanan, Kosmidis, and Dellaportas

Jorge Mateu’s contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’ by Narayanan, Kosmidis, and Dellaportas

Jorge Mateu’s contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’ by Narayanan, Kosmidis, and Dellaportas

Paul Smith’s contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’ by Narayanan, Kosmidis, and Dellaportas

Paul Smith’s contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’ by Narayanan, Kosmidis, and Dellaportas

Mattia Stival and Lorenzo Schiavon’s contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’ by Narayanan, Kosmidis, and Dellaportas

Mattia Stival and Lorenzo Schiavon’s contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’ by Narayanan, Kosmidis, and Dellaportas

Granger causality-based cluster sequence mining for spatio-temporal causal relation mining

We proposed a method to extract causal relations of spatial clusters from multi-dimensional event sequence data, also known as a spatio-temporal point process. The proposed Granger cluster sequence mining algorithm identifies the pairs of spatial data clusters that have causality over time with each other. It extended the cluster sequence mining algorithm, which utilized a statistical inference technique to identify the occurrence relation, with a causality inference based on the Granger causality. In addition, the proposed method utilizes a false discovery rate procedure to control the significance of the causality. Based on experiments on both synthetic and semi-real data, we confirmed that the algorithm is able to extract the synthetic causal relations from multiple different sets of data, even when disturbed with high level of spatial noise. False discovery rate procedure also helps to increase the accuracy even more under such case and also make the algorithm less-sensitive to the hyperparameters.

Spatio-Temporal Graph Neural Point Process for Traffic Congestion Event Prediction

Traffic congestion event prediction is an important yet challenging task in intelligent transportation systems. Many existing works about traffic prediction integrate various temporal encoders and graph convolution networks (GCNs), called spatio-temporal graph-based neural networks, which focus on predicting dense variables such as flow, speed and demand in time snapshots, but they can hardly forecast the traffic congestion events that are sparsely distributed on the continuous time axis. In recent years, neural point process (NPP) has emerged as an appropriate framework for event prediction in continuous time scenarios. However, most conventional works about NPP cannot model the complex spatio-temporal dependencies and congestion evolution patterns. To address these limitations, we propose a spatio-temporal graph neural point process framework, named STGNPP for traffic congestion event prediction. Specifically, we first design the spatio-temporal graph learning module to fully capture the long-range spatio-temporal dependencies from the historical traffic state data along with the road network. The extracted spatio-temporal hidden representation and congestion event information are then fed into a continuous gated recurrent unit to model the congestion evolution patterns. In particular, to fully exploit the periodic information, we also improve the intensity function calculation of the point process with a periodic gated mechanism. Finally, our model simultaneously predicts the occurrence time and duration of the next congestion. Extensive experiments on two real-world datasets demonstrate that our method achieves superior performance in comparison to existing state-of-the-art approaches.

Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems

Theoretical and applied cancer studies that use individual-based models (IBMs) have been limited by the lack of a mathematical formulation that enables rigorous analysis of these models. However, spatial cumulant models (SCMs), which have arisen from theoretical ecology, describe population dynamics generated by a specific family of IBMs, namely spatio-temporal point processes (STPPs). SCMs are spatially resolved population models formulated by a system of differential equations that approximate the dynamics of two STPP-generated summary statistics: first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances). We exemplify how SCMs can be used in mathematical oncology by modelling theoretical cancer cell populations comprising interacting growth factor-producing and non-producing cells. To formulate model equations, we use computational tools that enable the generation of STPPs, SCMs and mean-field population models (MFPMs) from user-defined model descriptions (Cornell et al. Nat Commun 10:4716, 2019). To calculate and compare STPP, SCM and MFPM-generated summary statistics, we develop an application-agnostic computational pipeline. Our results demonstrate that SCMs can capture STPP-generated population density dynamics, even when MFPMs fail to do so. From both MFPM and SCM equations, we derive treatment-induced death rates required to achieve non-growing cell populations. When testing these treatment strategies in STPP-generated cell populations, our results demonstrate that SCM-informed strategies outperform MFPM-informed strategies in terms of inhibiting population growths. We thus demonstrate that SCMs provide a new framework in which to study cell-cell interactions, and can be used to describe and perturb STPP-generated cell population dynamics. We, therefore, argue that SCMs can be used to increase IBMs’ applicability in cancer research.

Guest Editorial Robust Learning of Spatio-Temporal Point Processes: Modeling, Algorithm, and Applications

Temporal data are ubiquitous in real-world applications, and they can be generally divided into two categories: 1) synchronous temporal data which are basically equivalent to time series data; and 2) the asynchronous data which are often in the form of event data with a time stamp in continuous time-space. In fact, the event data are often converted to the time series by aggregating the event count in equal time intervals in many previous approaches. While it is often of one’s greater interest to directly establish models based on the raw event data whose time stamps carry useful information, especially for those time-sensitive tasks, ranging from earthquake prediction, crime analysis, to infectious disease diffusion forecasting, etc. Developing the spatio-temporal point process and the related applications is the theme of this Special Issue, which treats an event as a point in the spatio-temporal space, with possibly extra attributes. The model captures the instantaneous happening rate of the events and their potential dependency. The derived use cases often refer to future events prediction, and causality estimation.

Asynchronous Spatiotemporal Spike Metric for Event Cameras.

Event cameras as bioinspired vision sensors have shown great advantages in high dynamic range and high temporal resolution in vision tasks. Asynchronous spikes from event cameras can be depicted using the marked spatiotemporal point processes (MSTPPs). However, how to measure the distance between asynchronous spikes in the MSTPPs still remains an open issue. To address this problem, we propose a general asynchronous spatiotemporal spike metric considering both spatiotemporal structural properties and polarity attributes for event cameras. Technically, the conditional probability density function is first introduced to describe the spatiotemporal distribution and polarity prior in the MSTPPs. Besides, a spatiotemporal Gaussian kernel is defined to capture the spatiotemporal structure, which transforms discrete spikes into the continuous function in a reproducing kernel Hilbert space (RKHS). Finally, the distance between asynchronous spikes can be quantified by the inner product in the RKHS. The experimental results demonstrate that the proposed approach outperforms the state-of-the-art methods and achieves significant improvement in computational efficiency. Especially, it is able to better depict the changes involving spatiotemporal structural properties and polarity attributes.