Point Process Research Articles

Mule deer mortality in the northern Great Plains in a landscape altered by oil and natural gas extraction

AbstractA worldwide increasing demand for renewable and non‐renewable energy resources has been ongoing since the mid‐1970s and is projected to increase for the next 2 decades. The effects of oil and natural gas development on wildlife mortality risk may play an important role in mule deer (Odocoileus hemionus) population dynamics. We evaluated the potential effects of oil and natural gas development on mortality risk of mule deer in western North Dakota and eastern Montana, USA. We assessed adult and juvenile female mule deer mortality risk with Poisson point process models using 265 deer fitted with global positioning system (GPS) radio‐collars that were deployed from 2013–2016. Mortality covariates included proportion of area disturbed by oil and natural gas development, distance to oil and natural gas development, distance to roads, temperature, snow depth, normalized difference vegetation index (NDVI), and age of deer. During the study there was no effect of oil and natural gas development or roads on mule deer mortality, though <1% of all deer locations were within 500 m of active drilling rigs. Mule deer mortality was greatest in winter and spring, and positively related to temperature during these seasons. Estimated annual adult survival probability was 0.79 (95% CI = 0.71–0.85). Given the strong influence of season and temperature variables on mortality risk, weather had the strongest influence on mule deer mortality during this study. Although we did not detect an effect of energy development on mule deer mortality, effects on space use resulting from development could influence deer dynamics in the region through displacement and could occur over longer time scales than we evaluated. This study can be used in pre‐development planning in a risk assessment framework to minimize effects of development on mule deer.

A Splitting Method for Nonlinear Filtering Problems with Diffusive and Point Process Observations

A Splitting Method for Nonlinear Filtering Problems with Diffusive and Point Process Observations

Testing truncation dependence: The Gumbel–Barnett copula

In studies on lifetimes, occasionally, the population contains statistical units that are born before the data collection has started. Left-truncated are units that deceased before this start. For all other units, the age at the study start often is recorded and we aim at testing whether this second measurement is independent of the genuine measure of interest, the lifetime. Our basic model of dependence is the one-parameter Gumbel–Barnett copula. For simplicity, the marginal distribution of the lifetime is assumed to be Exponential and for the age-at-study-start, namely the distribution of birth dates, we assume a Uniform. Also for simplicity, and to fit our application, we assume that units that die later than our study period, are also truncated. As a result from point process theory, we can approximate the truncated sample by a Poisson process and thereby derive its likelihood. Identification, consistency and asymptotic distribution of the maximum-likelihood estimator are derived. Testing for positive truncation dependence must include the hypothetical independence which coincides with the boundary of the copula’s parameter space. By non-standard theory, the maximum likelihood estimator of the exponential and the copula parameter is distributed as a mixture of a two- and a one-dimensional normal distribution. For the proof, the third parameter, the unobservable sample size, is profiled out. An interesting result is, that it differs to view the data as truncated sample, or, as simple sample from the truncated population, but not by much. The application are 55 thousand double-truncated lifetimes of German businesses that closed down over the period 2014 to 2016. The likelihood has its maximum for the copula parameter at the parameter space boundary so that the p-value of test is 0.5. The life expectancy does not increase relative to the year of foundation. Using a Farlie–Gumbel–Morgenstern copula, which models positive and negative dependence, finds that life expectancy of German enterprises even decreases significantly over time. A simulation under the condition of the application suggests that the tests retain the nominal level and have good power.

Partial Mobilization: Tracking Multilingual Information Flows amongst Russian Media Outlets and Telegram

In response to disinformation and propaganda from Russian online media following the invasion of Ukraine, Russian media outlets such as Russia Today and Sputnik News were banned throughout Europe. To maintain viewership, many of these Russian outlets began to heavily promote their content on messaging services like Telegram. In this work, we study how 16 Russian media outlets interacted with and utilized 732 Telegram channels throughout 2022. Leveraging the foundational model MPNet, DP-Means clustering, and Hawkes processes, we trace how narratives spread between news sites and Telegram channels. We show that news outlets not only propagate existing narratives through Telegram but that they source material from the messaging platform. For example, across the websites in our study, between 2.3% (ura.news) and 26.7% (ukraina.ru) of articles discussed content that originated/resulted from activity on Telegram. Finally, tracking the spread of individual topics, we measure the rate at which news outlets and Telegram channels disseminate content within the Russian media ecosystem, finding that websites like ura.news and Telegram channels such as @genshab are the most effective at disseminating their content.

The statistical and dynamic modeling of the first part of the 2013-2014 Euromaidan protests in Ukraine: The Revolution of Dignity and preceding times.

Ukraine's tug-of-war between Russia and the West has had significant and lasting consequences for the country. In 2013, Viktor Yanukovych, the Ukrainian president aligned with Russia, opted against signing an association agreement with the European Union. This agreement aimed to facilitate trade and travel between the EU and Ukraine. This decision sparked widespread protests that coalesced in Kyiv's Maidan Square, eventually becoming known as the Euromaidan protests. In this study, we analyze the protest data from 2013, sourced from Ukraine's Center for Social and Labor Research. Despite the dataset's limitations and occasional inconsistencies, we demonstrate the extraction of valuable insights and the construction of a descriptive model from such data. Our investigation reveals a pre-existing state of self-excitation within the system even before the onset of the Euromaidan protests. This self-excitation intensified during the Euromaidan protests. A statistical analysis indicates that the government's utilization of force correlates with increased future protests, exacerbating rather than quelling the protest movement. Furthermore, we introduce the implementation of Hawkes process models to comprehend the spatiotemporal dynamics of the protest activity. Our findings highlight that, while protest activities spread across the entire country, the driving force behind the dynamics of these protests was the level of activity in Kyiv. Furthermore, in contrast to prior research that emphasized geographical proximity as a key predictor of event propagation, our study illustrates that the political alignment among oblasts, which are the distinct municipalities comprising Ukraine, had a more profound impact than mere geographic distance. This underscores the significance of social and cultural factors in molding the trajectory of political movements.

On the Characteristic Polynomial of the Eigenvalue Moduli of Random Normal Matrices

AbstractWe study the characteristic polynomial $$p_{n}(x)=\prod _{j=1}^{n}(|z_{j}|-x)$$ p n ( x ) = ∏ j = 1 n ( | z j | - x ) where the $$z_{j}$$ z j are drawn from the Mittag–Leffler ensemble, i.e. a two-dimensional determinantal point process which generalizes the Ginibre point process. We obtain precise large n asymptotics for the moment generating function $$\mathbb {E}[e^{\frac{u}{\pi } \, \text {Im\,}\ln p_{n}(r)}e^{a \, \text {Re\,}\ln p_{n}(r)}]$$ E [ e u π Im\, ln p n ( r ) e a Re\, ln p n ( r ) ] , in the case where r is in the bulk, $$u \in \mathbb {R}$$ u ∈ R and $$a \in \mathbb {N}$$ a ∈ N . This expectation involves an $$n \times n$$ n × n determinant whose weight is supported on the whole complex plane, is rotation-invariant, and has both jump- and root-type singularities along the circle centered at 0 of radius r. This “circular" root-type singularity differs from earlier works on Fisher–Hartwig singularities, and surprisingly yields a new kind of ingredient in the asymptotics, the so-called associated Hermite polynomials.

A stochastic model for the early stages of highly contagious epidemics by using a state-dependent point process

The recent COVID-19 pandemic has shown that when the reproduction number is high and there are no proper measurements in place, the number of infected people can increase dramatically in a short time, producing a phenomenon that many stochastic SIR-like models cannot describe: overdispersion of the number of infected people (i.e., the variance of the number of infected people during any interval is very high compared to the average). To address this issue, in this paper we explore the possibility of modeling the total number of infections as a state-dependent self-exciting point process. In this way, infections are not independent among themselves, but any infection will increase the likelihood of a new infection while also the number of currently infected and recovered individuals are included into determining the likelihood of new infections, Since long term simulation is extremely computationally intensive, exact expressions for the moments of the processes determining the number of infected and recovered individuals are computed, while also simulation algorithms for these state-dependent processes are provided.

Pricing VIX options based on mean-reverting models driven by information

Financial time series are dynamic and influenced by different types of information from the market. In this study, we propose new models for SPX and VIX options using the Hawkes process, jump process with stochastic intensity, and tempered stable process to capture these changes in financial time series based on three distinct characteristics of market information. We calculate the VIX option pricing formula using these models and find that the simplified VIX model based on VIX characteristics has significantly less pricing error than the consistent VIX model derived from the SPX model. Additionally, our findings suggest that the tempered stable process effectively models the volatility of VIX, sparse large jumps, and infinitesimal jumps. It also shows potential as an alternative to Brownian motion for representing volatility. Conversely, jump processes with stochastic jump intensities adeptly describe asymmetric jumps, and their integration with Brownian motion provides a more accurate depiction of the VIX’s volatility and jump dynamics. Finally, the introduction of jump processes into mean-reverting models for the VIX indicates a relatively low correlation between volatility magnitudes and the current VIX levels. This research contributes to the theory of SPX and VIX options and offers guidance for the development of other information-driven economic models.

(Almost) complete characterization of the stability of a discrete-time Hawkes process with inhibition and memory of length two

Abstract We consider a Poisson autoregressive process whose parameters depend on the past of the trajectory. We allow these parameters to take negative values, modelling inhibition. More precisely, the model is the stochastic process $(X_n)_{n\ge0}$ with parameters $a_1,\ldots,a_p \in \mathbb{R}$ , $p\in\mathbb{N}$ , and $\lambda \ge 0$ , such that, for all $n\ge p$ , conditioned on $X_0,\ldots,X_{n-1}$ , $X_n$ is Poisson distributed with parameter $(a_1 X_{n-1} + \cdots + a_p X_{n-p} + \lambda)_+$ . This process can be regarded as a discrete-time Hawkes process with inhibition and a memory of length p. In this paper we initiate the study of necessary and sufficient conditions of stability for these processes, which seems to be a hard problem in general. We consider specifically the case $p = 2$ , for which we are able to classify the asymptotic behavior of the process for the whole range of parameters, except for boundary cases. In particular, we show that the process remains stochastically bounded whenever the solution to the linear recurrence equation $x_n = a_1x_{n-1} + a_2x_{n-2} + \lambda$ remains bounded, but the converse is not true. Furthermore, the criterion for stochastic boundedness is not symmetric in $a_1$ and $a_2$ , in contrast to the case of non-negative parameters, illustrating the complex effects of inhibition.

HP-LSTM: Hawkes Process–LSTM-Based Detection of DDoS Attack for In-Vehicle Network

Connected and autonomous vehicles (CAVs) are advancing at a fast speed with the improvement of the automotive industry, which opens up new possibilities for different attacks. A Distributed Denial-of-Service (DDoS) attacker floods the in-vehicle network with fake messages, resulting in the failure of driving assistance systems and impairment of vehicle control functionalities, seriously disrupting the normal operation of the vehicle. In this paper, we propose a novel DDoS attack detection method for in-vehicle Ethernet Scalable service-Oriented Middleware over IP (SOME/IP), which integrates the Hawkes process with Long Short-Term Memory networks (LSTMs) to capture the dynamic behavioral features of the attacker. Specifically, we employ the Hawkes process to capture features of the DDoS attack, with its parameters reflecting the dynamism and self-exciting properties of the attack events. Subsequently, we propose a novel deep learning network structure, an HP-LSTM block, inspired by the Hawkes process, while employing a residual attention block to enhance the model’s detection efficiency and accuracy. Additionally, due to the scarcity of publicly available datasets for SOME/IP, we employed a mature SOME/IP generator to create a dataset for evaluating the validity of the proposed detection model. Finally, extensive experiments were conducted to demonstrate the effectiveness of the proposed DDoS attack detection method.

The Spatial Scale and Spread of Child Victimization.

Previous research shows that large, densely populated urban areas have higher rates of child victimization that have persisted over time. However, few investigations have inquired about the processes that produce and sustain hot and cold spots of child victimization. As a result, the mechanisms that produce the observed spatial clustering of child victimization, and hence "why" harms against children tend to cluster in space, remains unknown. Does the likelihood of being a victim of violence in one location depend on a similar event happening in a nearby location within a specified timeframe? Rather, are child victims of violence more likely to reside in suboptimal neighborhood conditions? This paper aims to present an analytical and theoretical framework for distinguishing between these locational (point) processes to determine whether the empirical spatial patterns undergirding child victimization are more reflective of the "spread" via contagion (i.e., dependency) or whether they are produced by neighborhood structural inequality resulting from spatial heterogeneity. To detect spatial dependence, we applied the inhomogeneous K-function to Los Angeles Medical Examiner data on child homicide victim locations while controlling for regional differences in victimization events (i.e., heterogeneity). Our analysis found strong evidence of spatial clustering in child victimization at small spatial scales but inhibition at larger scales. We further found limited support for the spatiotemporal clustering of child victimization indicative of a contagion effect. Overall, our results support the role of neighborhood structural vulnerability in the underlying mechanisms producing patterns of child victimization across Los Angeles County. We conclude by discussing the policy implications for understanding this spatial patterning in geographical context and for developing effective and targeted preventive interventions.

Evaluating spatial resolution and imperfect detection effects on the predictive performance of inhomogeneous spatial point process models trained with simulated presence-only data

Evaluating spatial resolution and imperfect detection effects on the predictive performance of inhomogeneous spatial point process models trained with simulated presence-only data

Interactions between different birds of prey as a random point process

The two-dimensional (2D) Coulomb gas is a one-parameter family of random point processes, depending on the inverse temperature β. Based on previous work, it is proposed as a simple statistical measure to quantify the intra- and interspecies repulsion among three different highly territorial birds of prey. Using data from the area of the Teutoburger Wald over 20 years, we fit the nearest-neighbour and next-to-nearest neighbour spacing distributions between the respective nests of the goshawk, eagle owl and the previously examined common buzzard to β of the Coulomb gas. Within each species, the repulsion measured in this way deviates significantly from the Poisson process of independent points in the plane. In contrast, the repulsion amongst each of two species is found to be considerably lower and closer to Poisson. Methodologically, we investigate the influence of the terrain, of a shorter interaction range given by the 2D Yukawa interaction, and the statistical independence of the time moving average we use for the yearly ensembles of occupied nests. We also check that an artificial random displacement of the original nest positions of the order of the mean level spacing quickly destroys the repulsion measured by β > 0. A simple, approximate analytical expression for the nearest-neighbour spacing distribution derived from non-Hermitian random matrix theory proves to be very useful.

Aging Renewal Point Processes and Exchangeability of Event Times

In this paper, we investigate the impact of latency aging on exchangeable (invariant under permutation of indices) inter-arrival times arising from mixed renewal point processes (statistical mixtures of point processes with renewal inter-arrival times) and explore the implications for reliability and survival analysis. We prove that aging preserves the exchangeability of inter-arrival times. Our data analysis, which includes both surrogate data and a Bayesian approach to high-frequency currency exchange-rate data, shows how aging impacts key survival analysis metrics such as failure survival, renewal, and hazard rate functions.

Asymptotics of the confluent hypergeometric process with a varying external potential in the super-exponential region

In this paper, we investigate a determinantal point process on the interval [Formula: see text], associated with the confluent hypergeometric kernel. Let [Formula: see text] denote the trace class integral operator acting on [Formula: see text] with the confluent hypergeometric kernel. Our focus is on deriving the asymptotics of the Fredholm determinant [Formula: see text] as [Formula: see text], while simultaneously [Formula: see text] in a super-exponential region. In this regime of double scaling limit, our asymptotic result also gives us asymptotics of the eigenvalues [Formula: see text] of the integral operator [Formula: see text] as [Formula: see text]. Based on the integrable structure of the confluent hypergeometric kernel, we derive our asymptotic results by applying the Deift–Zhou nonlinear steepest descent method to analyze the related Riemann–Hilbert problem.

Cox processes driven by transformed Gaussian processes on linear networks—A review and new contributions

Cox processes driven by transformed Gaussian processes on linear networks—A review and new contributions

An Inhomogeneous Weibull–Hawkes Process to Model Underdispersed Acoustic Cues

AbstractA Hawkes point process describes self-exciting behaviour where event arrivals are triggered by historic events. These models are increasingly becoming a popular choice in analysing event-type data. Like all other inhomogeneous Poisson point processes, the waiting time between events in a Hawkes process is derived from an exponential distribution with mean one. However, as with many ecological and environmental data, this is an unrealistic assumption. We, therefore, extend and generalise the Hawkes process to account for potential under- or overdispersion in the waiting times between events by assuming the Weibull distribution as the foundation of the waiting times. We apply this model to the acoustic cue production times of sperm whales and show that our Weibull–Hawkes model better captures the inherent underdispersion in the interarrival times of echolocation clicks emitted by these whales.

Preface: ISPRS Technical Commission I Midterm Symposium on “Intelligent Sensing and Remote Sensing Application”

Abstract. The ISPRS Technical Commission I Midterm Symposium on "Intelligent Sensing and Remote Sensing Application" was held in Changsha, China, during May 13–17, 2024, aiming to provide a platform to share the latest researches, advanced technologies and application experience, to discuss the future development and to seek international cooperation in various forms. The Symposium has received 229 full paper and abstract s, among them 45 double-blind peer-reviewed full papers were published in ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information, and 165 papers accepted through abstract review were published in the International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. These papers are mostly dedicated to topics of the 8 TC I Working Groups, 3 Inter-commission Working Groups, including Satellite Missions and Constellations for Remote Sensing, Mobile Mapping Technology, Multispectral, Hyperspectral and Thermal Sensors, LiDAR, Laser Altimetry and Sensor Integration, Microwave and InSAR Technology for Earth Observation, Orientation, Calibration and Validation of Sensors, Data Quality and Benchmark of Sensors, Multi-sensor Modelling and Cross-modality Fusion, Robotics for Mapping and Machine Intelligence, Autonomous Sensing Systems and their Applications, Digital Construction: Reality Capture, Automated Inspection and Integration to BIM, Point Cloud Generation and Processing, Artificial Intelligence Technology Related to Sensor Systems, Multi-sensor Remote Sensing Applications.. These papers presented the latest trends of sensor systems. The full papers and abstracts were reviewed by the members of the Symposium Scientific Committee comprised of Working Group officers and invited experts. We would like to take this opportunity to express our great gratitude to the Scientific Committee, Local Organizing Committee, Sponsors, Exhibitors and all those who have contributed to this successful Symposium. We also want to express our thanks to the authors for their excellent papers and presentations. Tang Xinming, Antonio Maria Garcia Tommaselli, Zhang Tao, Xie JunfengISPRS Technical Commission I on Sensor SystemsMay 2024, Changsha, China

Credit default swap pricing with counterparty risk in a reduced form model with Hawkes process

Credit default swap pricing with counterparty risk in a reduced form model with Hawkes process

Preface: ISPRS Technical Commission I Midterm Symposium on “Intelligent Sensing and Remote Sensing Application”

Abstract. The ISPRS Technical Commission I Midterm Symposium on "Intelligent Sensing and Remote Sensing Application" was held in Changsha, China, during May 13–17, 2024, aiming to provide a platform to share the latest researches, advanced technologies and application experience, to discuss the future development and to seek international cooperation in various forms. The Symposium has received 229 full paper and abstract s, among them 45 double-blind peer-reviewed full papers were published in ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information, and 165 papers accepted through abstract review were published in the International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. These papers are mostly dedicated to topics of the 8 TC I Working Groups, 3 Inter-commission Working Groups, including Satellite Missions and Constellations for Remote Sensing, Mobile Mapping Technology, Multispectral, Hyperspectral and Thermal Sensors, LiDAR, Laser Altimetry and Sensor Integration, Microwave and InSAR Technology for Earth Observation, Orientation, Calibration and Validation of Sensors, Data Quality and Benchmark of Sensors, Multi-sensor Modelling and Cross-modality Fusion, Robotics for Mapping and Machine Intelligence, Autonomous Sensing Systems and their Applications, Digital Construction: Reality Capture, Automated Inspection and Integration to BIM, Point Cloud Generation and Processing, Artificial Intelligence Technology Related to Sensor Systems, Multi-sensor Remote Sensing Applications.. These papers presented the latest trends of sensor systems. The full papers and abstracts were reviewed by the members of the Symposium Scientific Committee comprised of Working Group officers and invited experts. We would like to take this opportunity to express our great gratitude to the Scientific Committee, Local Organizing Committee, Sponsors, Exhibitors and all those who have contributed to this successful Symposium. We also want to express our thanks to the authors for their excellent papers and presentations. Tang Xinming, Antonio Maria Garcia Tommaselli, Zhang Tao, Xie JunfengISPRS Technical Commission I on Sensor SystemsMay 2024, Changsha, China