Spatio-temporal Point Process Research Articles

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.

Testing the first-order separability hypothesis for spatio-temporal point patterns

First-order separability of a spatio-temporal point process plays a fundamental role in the analysis of spatio-temporal point pattern data. While it is often a convenient assumption that simplifies the analysis greatly, existing non-separable structures should be accounted for in the model construction. Three different tests are proposed to investigate this hypothesis as a step of preliminary data analysis. The first two tests are exact or asymptotically exact for Poisson processes. The first test based on permutations and global envelopes allows one to detect at which spatial and temporal locations or lags the data deviate from the null hypothesis. The second test is a simple and computationally cheap χ2-test. The third test is based on stochastic reconstruction method and can be generally applied for non-Poisson processes. The performance of the first two tests is studied in a simulation study for Poisson and non-Poisson models. The third test is applied to the real data of the UK 2001 epidemic foot and mouth disease.1

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.

Conditional intensity: A powerful tool for modelling and analysing point process data

SummaryThe conditional intensity function of a spatial point process describes how the probability that a point of the process occurs ‘at’ a particular point in its carrier space depends on the realisation of the process in the remainder of the carrier space. Provided that the point process is simple, the conditional intensity determines all of the properties of the process, in particular its likelihood function. In this paper, we review the use of the conditional intensity function in the formulation of point process models and in making inferences from point process data, giving separate consideration to temporal, spatial and spatiotemporal settings. We argue that the conditional intensity function should take centre‐stage in spatiotemporal point process modelling and analysis.

Iberian oak decline caused by Phytophthora cinnamomi: A spatiotemporal analysis incorporating the effect of host heterogeneities at landscape scale

AbstractThe pathogen Phytophthora cinnamomi is considered a main driver of Iberian oak decline (IOD), a forest disease which decimates holm oaks (Quercus ilex) and cork oaks (Quercus suber) in a multipurpose, silvo‐pastoral and seminatural ecosystem of 3.1 million hectares in the south‐west of Europe. Little is known about the spatial dynamics of Phytophthora cinnamomi and how forest stand characteristics affect the IOD epidemic. Here, we analyse IOD spread over several decades in one such ecosystem by means of a multilevel approach based on (a) identification of diseased sites via repeated aerial imagery at landscape scale, (b) confirmation by subsampling of soil and roots, and iii) an epidemic model accounting for host population heterogeneities. We use a 'self‐exciting' spatiotemporal point process with two additive risk components: an epidemic component represents the inoculum pressure from nearby disease foci, and a background component describes sporadic disease transmission over larger distances or from unobserved sources. Both risk components are found to increase over time, and a lagged power‐law spatial kernel provides the best fit for the observed disease pattern. We estimate that 49% of the secondary infections triggered by a primary source occur within a distance of 250 m. Our results also highlight the role of density and diversity of the host population; we find that the rate of sporadic infections in silvo‐pastoral systems (dehesas) is lower than in forests, and higher in mixed stands and shrub encroached oak lands than in pure stands. These results have direct implications for IOD management, for example the estimated spatial kernel may guide the definition of suitable target areas for localized control measures and help to quantify their success. Our results also suggest that silviculture treatments aimed at controlling the density and species composition of oak stands, as well as the abundance of shrubs, are crucial to the containment of IOD.

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.

A Non-Parametric Hawkes Process Model of Primary and Secondary Accidents on a UK Smart Motorway

Abstract A self-exciting spatiotemporal point process is fitted to incident data from the UK National Traffic Information Service to model the rates of primary and secondary accidents on the M25 motorway in a 12-month period during 2017–2018. This process uses a background component to represent primary accidents, and a self-exciting component to represent secondary accidents. The background consists of periodic daily and weekly components, a spatial component and a long-term trend. The self-exciting components are decaying, unidirectional functions of space and time. These components are determined via kernel smoothing and likelihood estimation. Temporally, the background is stable across seasons with a daily double peak structure reflecting commuting patterns. Spatially, there are two peaks in intensity, one of which becomes more pronounced during the study period. Self-excitation accounts for 6–7% of the data with associated time and length scales around 100 min and 1 km, respectively. In-sample and out-of-sample validation are performed to assess the model fit. When we restrict the data to incidents that resulted in large speed drops on the network, the results remain coherent.

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.

Graphical modelling and partial characteristics for multitype and multivariate-marked spatio-temporal point processes

A method for dealing with multivariate analysis of marked spatio-temporal point processes is presented by introducing different partial point characteristics, and by extending the spatial dependence graph model formalism. The approach yields a unified framework for different types of spatio-temporal data, including both, purely qualitatively (multivariate) cases and multivariate cases with additional quantitative marks. The proposed graphical model is defined through partial spectral density characteristics; it is highly computationally efficient and reflects the conditional similarity amongst sets of spatio-temporal sub-processes of either points or marked points with identical discrete marks. Two applications, on crime and forestry data, are presented.

Marked spatio-temporal point patterns, periodicity analysis and earthquakes: an analytical extension including hypocenter depth

The longitude, latitude and depth of the hypocenter in 3-D space and the date and time of rupture makes an earthquake a “point” in a spatio-temporal point pattern, observed over a region and months, years or decades. The magnitude of earthquakes marks the point pattern, as would hypocenter depth do if only the longitude and latitude of epicenters were used for location in 2-D space. Stochastic declustering, based on a space–time ETAS model (ETAS: epidemic-type aftershock sequence), is a procedure that can be applied in the preliminary stage of an earthquake catalog data analysis. Stochastic declustering procedures have underlying assumptions, such as the time independence of the background intensity function whether the spatial framework is 2-D or 3-D, and a separate treatment of hypocenter depth from longitude and latitude when the spatial framework is 3-D. Cyclical processes in the Earth, including tides and seasonal surface water loads, can introduce periodic behavior in earthquake occurrence and related variables. The effects of ETAS-based 2-D and 3-D declustering on the outcome of periodicity analyses performed from the resulting earthquake data catalogs are studied. The research objectives and statistical challenges include the detection of periodicities for hypocenter depth in addition to monthly earthquake number, and the risk of missing observations for hypocenter depth when the monthly earthquake number after declustering is zero. A version of the method of multi-frequential periodogram analysis (MFPA) that allows for missing observations in the input temporal series is presented in detail, and applied to hypocenter depth (monthly mean and median) for central and northern California from January 2006 to December 2014. The results obtained for the 2-D and 3-D declustered catalogs are compared with those for the original catalog for this region. A semiannual periodicity in hypocenter depth is detected for the original and 2-D declustered catalogs, and fitted with the goal of relating it to periodicities found in the time series of monthly earthquake numbers. Using these results for central and northern California earthquakes, some of the assumptions on the intensity function of the spatio-temporal point process in stochastic declustering are discussed and future research perspectives are proposed.

Mathematical and simulation methods for deriving extinction thresholds in spatial and stochastic models of interacting agents

Abstract In ecology, one of the most fundamental questions relates to the persistence of populations, or conversely to the probability of their extinction. Deriving extinction thresholds and characterizing other critical phenomena in spatial and stochastic models is highly challenging, with few mathematically rigorous results being available for discrete‐space models such as the contact process. For continuous‐space models of interacting agents, to our knowledge no analytical results are available concerning critical phenomena, even if continuous‐space models can arguably be considered to be more natural descriptions of many ecological systems than lattice‐based models. Here we present both mathematical and simulation‐based methods for deriving extinction thresholds and other critical phenomena in a broad class of agent‐based models called spatiotemporal point processes. The mathematical methods are based on a perturbation expansion around the so‐called mean‐field model, which is obtained at the limit of large‐scale interactions. The simulation methods are based on examining how the mean time to extinction scales with the domain size used in the simulation. By utilizing a constrained Gaussian process fitted to the simulated data, the critical parameter value can be identified by asking when the scaling between logarithms of the time to extinction and the domain size switches from sublinear to superlinear. As a case study, we derive the extinction threshold for the spatial and stochastic logistic model. The mathematical technique yields rigorous approximation of the extinction threshold at the limit of long‐ranged interactions. The asymptotic validity of the approximation is illustrated by comparing it to simulation experiments. In particular, we show that species persistence is facilitated by either short or long spatial scale of the competition kernel, whereas an intermediate scale makes the species vulnerable to extinction. Both the mathematical and simulation methods developed here are of very general nature, and thus we expect them to be valuable for predicting many kinds of critical phenomena in continuous‐space stochastic models of interacting agents, and thus to be of broad interest for research in theoretical ecology and evolutionary biology.

Further results on why a point process is effective for estimating correlation between brain regions

Signals from brain functional magnetic resonance imaging (fMRI) can be efficiently represented by a sparse spatiotemporal point process, according to a recently introduced heuristic signal processing scheme. This approach has already been validated for relevant conditions, demonstrating that it preserves and compresses a surprisingly large fraction of the signal information. Here we investigated the conditions necessary for such an approach to succeed, as well as the underlying reasons, using real fMRI data and a simulated dataset. The results show that the key lies in the temporal correlation properties of the time series under consideration. It was found that signals with slowly decaying autocorrelations are particularly suitable for this type of compression, where inflection points contain most of the information.

Tornado Occurrences in the United States: A Spatio-Temporal Point Process Approach

In this paper, we analyze the tornado occurrences in the Unites States. To perform inference procedures for the spatio-temporal point process we adopt a dynamic representation of Log-Gaussian Cox Process. This representation is based on the decomposition of intensity function in components of trend, cycles, and spatial effects. In this model, spatial effects are also represented by a dynamic functional structure, which allows analyzing the possible changes in the spatio-temporal distribution of the occurrence of tornadoes due to possible changes in climate patterns. The model was estimated using Bayesian inference through the Integrated Nested Laplace Approximations. We use data from the Storm Prediction Center’s Severe Weather Database between 1954 and 2018, and the results provided evidence, from new perspectives, that trends in annual tornado occurrences in the United States have remained relatively constant, supporting previously reported findings.

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.

Using the intrinsic growth rate of the mosquito population improves spatio-temporal dengue risk estimation

Understanding geographic population dynamics of mosquitoes is an essential requirement for estimating the risk of mosquito-borne disease transmission and geographically targeted interventions. However, the use of population dynamics measures, such as the intrinsic growth rate, as predictors in spatio-temporal point processes has not been investigated before. In this work we compared the predictive accuracy of four spatio-temporal log-Gaussian Cox models: (i) With no predictors; (ii) mosquito abundance as predictor; (iii) intrinsic growth rate as predictor; (iv) intrinsic growth rate and mosquito abundance as predictors. This analysis is based on Aedes aegypti mosquito surveillance and human dengue data obtained from the urban area of Caratinga, Brazil. We used a statistical Moran Curve approach to estimate the intrinsic growth rate and a zero inflated Poisson kriging model for estimating mosquito abundance at locations of dengue cases. The incidence of dengue cases was positively associated with mosquito intrinsic growth rate and this model outperformed, in terms of predictive accuracy, the abundance and the null models. The latter includes only the spatio-temporal random effect but no predictors. In the light of these results we suggest that the intrinsic growth rate should be investigated further as a potential tool for predicting the risk of dengue transmission and targeting health interventions for vector-borne diseases.

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.

Problem-driven spatio-temporal analysis and implications for postgraduate statistics teaching

The paper uses two case-studies, one in public health surveillance the other in veterinary epidemiology, to argue that the analysis strategy for spatio-temporal point process data should be guided by the scientific context in which the data were generated and, more particularly, by the objectives of the data analysis. This point of view is not specific to the point process setting and, in the author’s opinion, should influence the way that statistics is taught at postgraduate level in response to the emergence and rapid growth of data science.

First- and Second-Order Characteristics of Spatio-Temporal Point Processes on Linear Networks

We present several characteristics for spatio-temporal point patterns when the spatial locations are restricted to a linear network. A nonparametric kernel-based intensity estimator is proposed to highlight the concentration of events within the network and time, either jointly or separately. We also provide second-order characteristics for spatio-temporal point patterns on linear networks such as K-function and pair correlation function to analyze the type of interaction between points. They are independent of network’s geometry and have known values for Poisson point processes. Finally, we consider some applications to traffic accidents and demonstrate our findings by analyzing datasets of Houston (United States), Medellín (Colombia), and Eastbourne (United Kingdom). Supplementary materials for this article are available online.