Spatio-temporal Point Process Model Research Articles

Predicting urban signal-controlled intersection congestion events using spatio-temporal neural point process

ABSTRACT The urban traffic signal-controlled intersections are of great significance for solving the problem of urban road congestion. Previous research on congestion prediction mainly aggregated data at the level of road segments or traffic flow at a coarse regulated time interval. Fine-grained prediction of congestion events at the lane-level and cycle-level enables detailed a understanding of spatio-temporal dependencies, leading to congestion reduction, improved efficiency. This paper presents a Spatio-Temporal Neural Point Process (STNPP) model that combines Graph Neural Networks and Neural Temporal Point Process to predict congestion events at urban intersections. The proposed model allows for complete prediction of congestion events, including their occurrence, development, dissipation. In the process of spatial correlation modeling, graph neural networks are used to model the spatial relationships between both region and intersections. The current intersection and its upstream/downstream areas are modeled separately. To model the temporal correlations at individual intersections, we focus on a specific lane and capture the evolution of congestion events using the Neural Point Process Gated Recurrent Unit (NPPGRU), which captures the temporal granularity changes of signal-controlled cycles in congestion events. Using actual traffic speed and signal-controlled data from Hangzhou city, we validate that the proposed method achieves stable predictive performance.

Convolutional Non-Homogeneous Poisson Process and its Application to Wildfire Ignition Risk Quantification for Power Delivery Networks

To quantify wildfire ignition risks on power delivery networks, the current practice predominantly relies on the empirically calculated fire danger indices, which may not well capture the effects of dynamically changing environmental factors. This article proposes a spatio-temporal point process model, known as the Convolutional Non-homogeneous Poisson Process (cNHPP), and applies the model to quantify wildfire ignition risks for power delivery networks. The proposed model captures both the current (i.e., instantaneous) and cumulative (i.e., historical) effects of key environmental processes (i.e., covariates) on wildfire risks, as well as the spatio-temporal dependency among different segments of the power delivery network. The computation and interpretation of the intensity function are thoroughly investigated. We apply the proposed approach to estimate wildfire ignition risks on major transmission lines in California, using historical fire data, meteorological and vegetation data obtained from the National Oceanic and Atmospheric Administration and National Aeronautics and Space Administration. A comprehensive comparison study is performed to show the applicability and predictive capability of the proposed approach.

Unveiling Multi-Agent Strategies: A Data-Driven Approach for Extracting and Evaluating Team Tactics from Football Event and Freeze-Frame Data

Studying collective behavior in opposing multi-agent teams is crucial across game theory, robotics, and sports analytics. In sports, especially football, team tactics involve intricate strategic spatial and action behaviors displayed as event sequences during possession. Understanding and analyzing these tactics is essential for successful training, strategic planning, and on-field success. While traditional approaches, such as notational and statistical analyses, offer valuable insights into team tactics, they often lack a comprehensive consideration of contextual information, thereby limiting the holistic evaluation of teams’ performances. To bridge this gap and capture the nuanced intricacies of team tactics, we employed advanced methodologies. The sequential pattern mining algorithm PrefixSpan was utilized to extract tactical patterns from possession sequences, enabling a deeper understanding of how teams strategize and adapt during play. Additionally, the neural marked spatio temporal point process (NMSTPP) model was leveraged to model and predict team behaviors, facilitating a fair comparison among teams. The evaluation of team possessions was further enhanced through the innovative holistic possession utilization score metrics, providing a more nuanced assessment of performance. In our experimental exploration, we identified and classified five distinct team tactics, validated the efficacy of the NMSTPP model when integrating StatsBomb 360 data, and conducted a comprehensive analysis of English Premier League teams during the 2022/2023 season. The results were visualized using radar plots and scatter plots with mean shift clustering. Lastly, the potential applications to RoboCup were discussed.

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.

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.

Network self-exciting point processes to measure health impacts of COVID-19

AbstractThe assessment of the health impacts of the COVID-19 pandemic requires the consideration of mobility networks. To this aim, we propose to augment spatio-temporal point process models with mobility network covariates. We show how the resulting model can be employed to predict contagion patterns and to help in important decisions such as the distribution of vaccines. The application of the proposed methodology to 27 European countries shows that human mobility, along with vaccine doses and government policies, are significant predictors of the number of new COVID-19 reported infections and are therefore key variables for decision-making.

Atmospheric particulate matter effects on Sars-Cov-2 infection and its dynamics spreading: a spatio-temporal point process model

Background and Aim: Particulate matter (PM) may play a role in differential distribution and transmission rates of SARS-CoV-2. Identification of factors affecting the transmission dynamics concerning the endemic (persistent sporadic) and epidemic (rapidly clustered) component of infection can helps to implement intervention strategies to reduce the disease burden. Aim of this study is to assess the effect of long-term residential exposure to PM on Sars-Cov-2 incidence and on the dynamics of infectious disease spreading in Marche Region (Central Italy). Methods: All individuals with first positive SARS-CoV-2 molecular test from February to May 2020, residing in the Marche region were analysed along with gender, age, employment, Nursing Homes and Long-Term Care Facilities (NH-LTCF) residence and socio-economic deprivation index (DI); long-term exposure to outdoor PM ≤ 10 μm (PM10) concentrations, Temperature and Relative Humidity were estimated at 10 km2 grid cells. The endemic-epidemic spatio-temporal regression model for individual-level data was used to identify factors influencing SARS-CoV-2 spreading and its infectious rate. Rate ratios (RR) and 95% confidence intervals (CI) were calculated. Results: 10-years average exposure to PM10 was associated with an increased risk of new endemic (RR 1.14, 95%CI 1.04-1.24) and epidemic (RR 1.15, 95%CI 1.08-1.22) infectious. Male gender, older age, living in NH-LTCF and the worsening of DI increased RR in epidemic component. Lockdown increase the risk of becoming positive to Sars-Cov2 as concerning endemic while it reduces virus spreading in epidemic component. Increased temperature was associated with a reduction of endemic and epidemic infectious. Conclusions: Results show an increment of RR for exposure to increased levels of PM10 both in endemic and epidemic components. Targeted interventions are necessary to improve air quality in most polluted areas to minimize the burden of endemic and epidemic COVID-19 disease and to reduce unequal distribution of health risk. Keywords: air polltuion, Sars-Cov2, infectious disease

Spatiotemporal ETAS Model with a Renewal Main-Shock Arrival Process

AbstractWe propose a spatiotemporal point process model that enhances the classical Epidemic-Type Aftershock Sequence (ETAS) model. This is achieved with the introduction of a renewal main-shock arrival process and we call this extension the renewal ETAS (RETAS) model. This modification is similar in spirit to the renewal Hawkes (RHawkes) process but the conditional intensity process supports a spatial component. It empowers the main-shock intensity to reset upon the arrival of main-shocks. This allows for heavier clustering of main-shocks than the classical spatiotemporal ETAS model. We introduce a likelihood evaluation algorithm for parameter estimation and provide a novel procedure to evaluate the fitted model's goodness-of-fit (GOF) based on a sequential application of the Rosenblatt transformation. A simulation algorithm for the RETAS model is outlined and used to validate the numerical performance of the likelihood evaluation algorithm and GOF test procedure. We illustrate the proposed model and methods on various earthquake catalogues around the world each with distinctly different seismic activity. These catalogues demonstrate the RETAS model's additional flexibility in comparison to the classical spatiotemporal ETAS model and emphasizes the potential for superior modelling and forecasting of seismicity.

Atmospheric particulate matter effects on SARS-CoV-2 infection and spreading dynamics: A spatio-temporal point process model

Particulate matter (PM) may play a role in differential distribution and transmission rates of SARS-CoV-2. For public health surveillance, identification of factors affecting the transmission dynamics concerning the endemic (persistent sporadic) and epidemic (rapidly clustered) component of infection can help to implement intervention strategies to reduce the disease burden. The aim of this study is to assess the effect of long-term residential exposure to outdoor PM ≤ 10 μm (PM10) concentrations on SARS-CoV-2 incidence and on its spreading dynamics in Marche region (Central Italy) during the first wave of the COVID-19 pandemic (February to May 2020), using the endemic-epidemic spatio-temporal regression model for individual-level data. Environmental and climatic factors were estimated at 10 km2 grid cells.10-years average exposure to PM10 was associated with an increased risk of new endemic (Rate Ratio for 10 μg/m3 increase 1.14, 95%CI 1.04–1.24) and epidemic (Rate Ratio 1.15, 95%CI 1.08–1.22) infection. Male gender, older age, living in Nursing Homes and Long-Term Care Facilities residence and socio-economic deprivation index increased Rate Ratio (RR) in epidemic component. Lockdown increased the risk of becoming positive to SARS-CoV-2 as concerning endemic component while it reduced virus spreading in epidemic one. Increased temperature was associated with a reduction of endemic and epidemic infection.Results showed an increment of RR for exposure to increased levels of PM10 both in endemic and epidemic components. Targeted interventions are necessary to improve air quality in most polluted areas, where deprived populations are more likely to live, to minimize the burden of endemic and epidemic COVID-19 disease and to reduce unequal distribution of health risk.

Non-parametric comparative analysis of the spatiotemporal pattern of human-caused and natural wildfires in Galicia

Background Wildfire is a major environmental threat worldwide and climate change is expected to increase its severity. Galicia has suffered high wildfire incidence during the last decades, most wildfires being from arson, in contrast with the low rate of natural wildfires. Aim This work aims to characterise the spatiotemporal dynamics of human-caused and natural fires in Galicia. Methods We apply first- and second-order non-parametric inference to spatiotemporal wildfire point patterns. Key results The distribution of natural wildfires remained stable over years, with high incidence in summer and in the eastern area of Galicia. Arson wildfires had aggregated patterns, with strong interaction between outbreaks and fires, and their distribution varied both over and within years, with high incidence shifting between the southern and western areas, and high hazard in early spring and late summer. Negligence wildfire patterns showed short-distance aggregation, but large-distance aggregation between outbreaks and fires; their spatial distribution also varied between and within years. Conclusions Different models and covariates are required to predict the hazard from each wildfire type. Natural fires are linked to meteorological and environmental factors, whereas socioeconomic covariates are crucial in human-caused wildfires. Implications These results are the basis for the future development of predictive spatiotemporal point process models for human-caused wildfires.

Estimating koala density from incidental koala sightings in South-East Queensland, Australia (1997-2013), using a self-exciting spatio-temporal point process model.

The koala, Phascolarctos cinereus, is an iconic Australian wildlife species facing a rapid decline in South‐East Queensland (SEQLD). For conservation planning, the ability to estimate the size of koala populations is crucial. Systematic surveys are the most common approach to estimate koala populations but because of their cost they are often restricted to small geographic areas and are conducted infrequently. Public interest and participation in the collection of koala sighting data is increasing in popularity, but such data are generally not used for population estimation. We modeled monthly sightings of koalas reported by members of the public from 1997 to 2013 in SEQLD by developing a self‐exciting spatio‐temporal point process model. This allowed us to account for characteristics that are associated with koala presence (which vary over both space and time) while accounting for detection bias in the koala sighting process and addressing spatial clustering of observations. The density of koalas varied spatially due to the heterogeneous nature of koala habitat in SEQLD, with a mean density of 0.0019 koalas per km2 over the study period. The percentage of land areas with very low densities (0–0.0005 koalas per km2) remained similar throughout the study period representing, on average, 66% of the total study area. The approach described in this paper provides a useful starting point to allow greater use to be made of incidental koala sighting data. We propose that the model presented here could be used to combine systematic koala survey data (which is spatially restricted, but more precise) with koala sighting data (which is incidental and often biased by nature, but often collected over large geographical areas). Our approach could also be adopted for modeling the density of other wildlife species where data is collected in the same manner.

Learning to Be Creative: A Mutually Exciting Spatiotemporal Point Process Model for Idea Generation in Open Innovation

This study investigates the creative idea generation process in an open innovation platform. The idea generation process is simultaneously influenced by multiple activities: knowledge acquisition from participants’ interactions with each other’s ideas, deliberate practice through persistent participation, and learning through failures. Due to the dynamic interplay across these activities, it is challenging to identify each activity’s influence on creative ideation outcomes using reduced-form regression analysis. To overcome these challenges, we employ a comprehensive empirical framework, the mutually exciting spatiotemporal point process model with unobserved heterogeneity, which endogenizes the occurrences of these activities in continuous time and allows for user-dependent effects. By utilizing the activity stream data of 13,028 participants from 2010 to 2016 in an open innovation platform, we uncovered synergistic effects of these activities on creative outcomes. We find that knowledge acquired through interaction with others (i.e., stimulus ideas) plays a vital role in the creative ideation process, but their effect is more nuanced than what we have known so far. In contrast to the prior belief that distant analogies, stimulus ideas outside of a problem domain, spur creativity, we find that distant analogies lead to failures. Yet, we further find that such failures are indispensable to the creative ideation process because failures motivate idea generators (1) to acquire more knowledge by increasing their future interactions with other participants’ ideas (learning from others), and (2) to persist in generating ideas that lead to improvements in their ability to apply the acquired knowledge and to identify innovation tasks that are relevant to their stock of acquired knowledge (learning by doing). Our results indicate that failures are a stronger driver of the learning activities than successes. Based on our findings, we offer insights on how to cultivate creativity in an open innovation setting.

Analysis of local habitat selection and large-scale attraction/avoidance based on animal tracking data: is there a single best method?

BackgroundNew wildlife telemetry and tracking technologies have become available in the last decade, leading to a large increase in the volume and resolution of animal tracking data. These technical developments have been accompanied by various statistical tools aimed at analysing the data obtained by these methods.MethodsWe used simulated habitat and tracking data to compare some of the different statistical methods frequently used to infer local resource selection and large-scale attraction/avoidance from tracking data. Notably, we compared spatial logistic regression models (SLRMs), spatio-temporal point process models (ST-PPMs), step selection models (SSMs), and integrated step selection models (iSSMs) and their interplay with habitat and animal movement properties in terms of statistical hypothesis testing.ResultsWe demonstrated that only iSSMs and ST-PPMs showed nominal type I error rates in all studied cases, whereas SSMs may slightly and SLRMs may frequently and strongly exceed these levels. iSSMs appeared to have on average a more robust and higher statistical power than ST-PPMs.ConclusionsBased on our results, we recommend the use of iSSMs to infer habitat selection or large-scale attraction/avoidance from animal tracking data. Further advantages over other approaches include short computation times, predictive capacity, and the possibility of deriving mechanistic movement models.

Predicting new cases of COVID‐19 and the application to population sustainability analysis

We propose a new spatio‐temporal point process model to predict infectious cases of COVID‐19. We illustrate its practical use with data from six key cities in China, and we analyse the effects of natural and social factors on the occurrence and spread of COVID‐19. We show that large‐scale testing and strict containment are key factors for the successful suppression of the COVID‐19 contagion. This study provides an effective tool to develop early warning systems for major infectious diseases, offering insights on how to develop prevention and control strategies to reduce the impact of disease and maintain population sustainability.

A spatio-temporal multi-scale model for Geyer saturation point process: Application to forest fire occurrences

Because most natural phenomena exhibit dependence at multiple scales like locations of earthquakes or forest fire occurrences, spatio-temporal single-scale point process models are unrealistic in many applications. This motivates us to construct generalizations of classical Gibbs models. In this paper, we extend the Geyer saturation point process model to the spatio-temporal multi-scale framework. The simulation process is carried out through a birth–death Metropolis–Hastings algorithm. In a simulation study, we compare two common methods for statistical inference in Gibbs models: the pseudo-likelihood and logistic likelihood approaches that we tailor to this model. Finally, we illustrate this new model on forest fire occurrences modeling in Southern France.

Imitation Learning of Neural Spatio-Temporal Point Processes

We present a novel Neural Embedding Spatio-Temporal (NEST) point process model for spatio-temporal discrete event data and develop an efficient imitation learning (a type of reinforcement learning) based approach for model fitting. Despite the rapid development of one-dimensional temporal point processes for discrete event data, the study of spatial-temporal aspects of such data is relatively scarce. Our model captures complex spatio-temporal dependence between discrete events by carefully design a mixture of heterogeneous Gaussian diffusion kernels, whose parameters are parameterized by neural networks. This new kernel is the key that our model can capture intricate spatial dependence patterns and yet still lead to interpretable results as we examine maps of Gaussian diffusion kernel parameters. The imitation learning model fitting for the NEST is more robust than the maximum likelihood estimate. It directly measures the divergence between the empirical distributions between the training data and the model-generated data. Moreover, our imitation learning-based approach enjoys computational efficiency due to the explicit characterization of the reward function related to the likelihood function; furthermore, the likelihood function under our model enjoys tractable expression due to Gaussian kernel parameterization. Experiments based on real data show our method’s good performance relative to the state-of-the-art and the good interpretability of NEST’s result.

Network Self-Exciting Point Processes To Measure Health Impacts of COVID-19

The assessment of the health impacts of the COVID-19 pandemic requires the consideration of mobility networks. To this aim, we propose to augment spatio-temporal point process models with mobility network covariates. We show how the resulting model can be employed to predict contagion patterns and to help important decisions such as the distribution of vaccines. The application of the proposed methodology to 27 European countries shows that human mobility, along with vaccine doses and government policies, are significant predictors of the number of new COVID-19 reported infections and are therefore key variables for decision making.

Spatio-Temporal Point Process for Multiple Object Tracking.

Multiple object tracking (MOT) focuses on modeling the relationship of detected objects among consecutive frames and merge them into different trajectories. MOT remains a challenging task as noisy and confusing detection results often hinder the final performance. Furthermore, most existing research are focusing on improving detection algorithms and association strategies. As such, we propose a novel framework that can effectively predict and mask-out the noisy and confusing detection results before associating the objects into trajectories. In particular, we formulate such "bad" detection results as a sequence of events and adopt the spatio-temporal point process to model such events. Traditionally, the occurrence rate in a point process is characterized by an explicitly defined intensity function, which depends on the prior knowledge of some specific tasks. Thus, designing a proper model is expensive and time-consuming, with also limited ability to generalize well. To tackle this problem, we adopt the convolutional recurrent neural network (conv-RNN) to instantiate the point process, where its intensity function is automatically modeled by the training data. Furthermore, we show that our method captures both temporal and spatial evolution, which is essential in modeling events for MOT. Experimental results demonstrate notable improvements in addressing noisy and confusing detection results in MOT data sets. An improved state-of-the-art performance is achieved by incorporating our baseline MOT algorithm with the spatio-temporal point process model.

Animal movement models with mechanistic selection functions

A suite of statistical methods are used to study animal movement. Most of these methods treat animal telemetry data in one of three ways: as discrete processes, as continuous processes, or as point processes. We briefly review each of these approaches and then focus in on the latter. In the context of point processes, so-called resource selection analyses are among the most common way to statistically treat animal telemetry data. However, most resource selection analyses provide inference based on approximations of point process models. The forms of these models have been limited to a few types of specifications that provide inference about relative resource use and, less commonly, probability of use. For more general spatio-temporal point process models, the most common type of analysis often proceeds with a data augmentation approach that is used to create a binary data set that can be analyzed with conditional logistic regression. We show that the conditional logistic regression likelihood can be generalized to accommodate a variety of alternative specifications related to resource selection. We then provide an example of a case where a spatio-temporal point process model coincides with that implied by a mechanistic model for movement expressed as a partial differential equation derived from first principles of movement. We demonstrate that inference from this form of point process model is intuitive (and could be useful for management and conservation) by analyzing a set of telemetry data from a mountain lion in Colorado, USA, to understand the effects of spatially explicit environmental conditions on movement behavior of this species.

Learning to be Creative: A Mutually Exciting Spatial Point Process Model for Idea Generation in Open Innovation

This study investigates the creative idea generation process in an open innovation platform. Idea generation process is simultaneously influenced by multiple activities: knowledge acquisition from participants' interactions with each others' ideas, deliberate practice through persistent participation, and learning through failures. Due to the dynamic interplay across these activities, it is challenging to identify each activity's influence on creative ideation outcomes using reduced-form regression analysis. To overcome these challenges, we employ a comprehensive empirical framework, the mutually exciting spatio-temporal point process model with unobserved heterogeneity, which endogenizes the occurrences of these activities in continuous time and allows for user-dependent effects. By utilizing the activity stream data of 13,028 participants from 2010 to 2016 in an open innovation platform, we uncovered synergistic effects of these activities on creative outcomes. We find that knowledge acquired through interaction with others (i.e., stimulus ideas) plays a vital role in the creative ideation process, but their effect is more nuanced than what we have known so far. In contrast to the prior belief that distant analogies, stimulus ideas outside of a problem domain, spur creativity, we find that distant analogies lead to failures. Yet, we further find that such failures are indispensable to the creative ideation process because failures motivate idea generators (1) to acquire more knowledge by increasing their future interactions with other participants' ideas (learning from others), and (2) to persist in generating ideas that lead to improvements in their ability to apply the acquired knowledge and to identify innovation tasks that are relevant to their stock of acquired knowledge (learning by doing). Our results indicate that failures are a stronger driver of the learning activities than successes. Based on our findings, we offer insights on how to cultivate creativity in an open innovation setting.