Point Process Model Research Articles

A point-process model of tapping along to difficult rhythms

Experiments where participants synchronise their taps to rhythmic cues are often used to study human perception and performance of rhythms. This experimental study is novel in two regards: The cyclic rhythms (non-isochronous patterns of cues) presented to participants were more challenging than usual (including many from unfamiliar time signatures), and we have modelled participants’ performance via a conditional point process. Point processes are well suited to describing partly random sequences of events, but have rarely been used previously to model tapping experiments, the only other study we know being Cannon (2021). Our model uses continuous functional parameters to describe participants’ responses to auditory stimuli with much finer temporal resolution than in previous studies. Taking account of both the clock and the dynamic attention theories of sensorimotor synchronisation, we assessed the time course of the propensity to tap within each cycle at a resolution of less than 13ms, identifying the influence of cues on the tapping propensity and the progress of learning their rhythmic patterns. We also sought to determine the trajectory of the putative refractory period (feedback inhibition of tapping) after each tap, and assessed the distribution of tap-cue asynchronies in a more finely resolved manner than usual. Our models also indicated complex kinetics of the feedback over about 100ms.

Modeling the spatial evolution wildfires using random spread process

AbstractThe study of wildfire spread and the growth of the area burned is an important task in ecological studies and in other contexts. In this work we present a model for fire spread and show the results obtained from simulations of burned areas. The model is based on probabilities of fire at different locations. Such probabilities are obtained from the intensity function of a spatial point process model fitted to the observed pattern of fires in the Valencian Community for the years 1993–2015. The models, applied to different wildfires in Spain, including the different temporal states, combines the features of a network model with those of a quasi‐physical model of the interaction between burning and nonburning cells, which strongly depends on covariates. The results of the simulated wildfire burned areas resemble the burned areas observed in real cases, suggesting that the model proposed, based on a Markov process called Random Spread Process, works adequately. The model can be extended to simulate other random spread processes such as epidemics.

Higher order Gibbs point process modeling of 2005-Kashmir earthquakes

Higher order Gibbs point process modeling of 2005-Kashmir earthquakes

Detection Performance Evaluation for Marine Wireless Sensor Networks

Detection performance evaluation is one of the inevitable problems for marine wireless sensor networks (MWSNs) deployed for target detection. However, it is a very complicated problem since it associates many different aspects, such as emitter power, range, radar cross-section, weather, geography, working mode, and so on. Targeting this problem, this paper incorporates the Poisson point process model into describing the ranges from sensors to targets. The relationship between sensors and a target is built from the perspective of detection probabilities. Then, a new consistent, conservative target detection probability evaluation is derived within a CFAR framework, and the further global detection probability of the whole MWSN on the target is developed. Additionally, the rationality of this modeling approach is demonstrated via simulation results, which is in accord with the actual situation.

Drug Treatment Effect Model Based on MODWT and Hawkes Self-Exciting Point Process.

In precision medicine, especially in the pharmacodynamic area, the lack of an adequate long-term drug effect monitoring model leads to a quite low robustness to the instant drug treatment. Modelling the effect of drug based on the monitoring variables is essential to measure the drug benefit and its side effect preciously. In order to model the complex drug behavior in the context of time series, a sin function is selected to describe the basic trend of heart rate variable that is medically monitored. A Hawkes self-exciting point process model is chosen to describe the effect caused by multiple and sequential drug usage at different time points. The model considers the time lag between the drug given time and the drug effect during the whole drug emission period. A cumulative Gamma distribution is employed to describe the time lag effect. Simulation results demonstrate the established model effectively when describing the baseline trend and the drug effect with low noise levels, where the maximal overlap discrete wavelet transformation is utilized for the information decomposition in the frequency zone. The real data of the variables heart rate and drug liquemin from a medical database is analyzed. Instead of the original time series, scale variable s4 is selected according to the Granger cointegration test. The results show that the model accurately characterizes the cumulative drug effect with the Pearson correlation test value as 0.22, which is more significant for the value under 0.1. In the future, the model can be extended to more complicated scenarios through taking into account multiple monitoring variables and different kinds of drugs.

Pseudo-prospective testing of 5-year earthquake forecasts for California using inlabru

Abstract. Probabilistic earthquake forecasts estimate the likelihood of future earthquakes within a specified time-space-magnitude window and are important because they inform planning of hazard mitigation activities on different time scales. The spatial component of such forecasts, expressed as seismicity models, generally relies upon some combination of past event locations and underlying factors which might affect spatial intensity, such as strain rate, fault location and slip rate or past seismicity. For the first time, we extend previously reported spatial seismicity models, generated using the open source inlabru package, to time-independent earthquake forecasts using California as a case study. The inlabru approach allows the rapid evaluation of point process models which integrate different spatial datasets. We explore how well various candidate forecasts perform compared to observed activity over three contiguous 5-year time periods using the same training window for the input seismicity data. In each case we compare models constructed from both full and declustered earthquake catalogues. In doing this, we compare the use of synthetic catalogue forecasts to the more widely used grid-based approach of previous forecast testing experiments. The simulated catalogue approach uses the full model posteriors to create Bayesian earthquake forecasts, not just the mean. We show that simulated catalogue based forecasts perform better than the grid-based equivalents due to (a) their ability to capture more uncertainty in the model components and (b) the associated relaxation of the Poisson assumption in testing. We demonstrate that the inlabru models perform well overall over various time periods: The full catalogue models perform favourably in the first testing period (2006–2011) while the declustered catalogue models perform better in the 2011–2016 testing period, with both sets of models performing less well in the most recent (2016–2021) testing period. Together, these findings demonstrate a significant improvement in earthquake forecasting is possible although this has yet to be tested and proven in true prospective mode.

Combining models for animal tracking: Defining behavioural states to understand space use for conservation

AbstractAimRapid advances in technology have created tools able to explore how animals differ in their use of the environment based on behaviour, which can provide insights into the ecology of endangered animals and the threats they face. Though threatened, we know little of vultures' spatial ecology. We examine the external variables that affect vultures' decisions regarding space use, specifically during foraging and feeding when they are at greatest risk for encountering threats, and use this to inform effective conservation interventions.LocationTanzania, specifically Southern Tanzanian protected area networks.Taxon Gyps africanus. MethodsWe tracked 26 African white‐backed vultures between 2015 and 2019 in Southern Tanzania. Using hidden Markov models to identify behaviour from raw GPS points and point process models to spatially analyse these behaviours, we tested resource selection decisions in vultures during foraging and feeding, when they are at greatest risk of poisoning.ResultsAfrican white‐backed vultures are most likely to forage early in the day outside National Parks, specifically in Game Reserves and Wildlife Management Areas, but avoid areas with high livestock numbers to feed. Eastern and Western populations showed slight differences in preferences, highlighting the need for population level considerations. When not selecting for behaviour, closeness to rivers and habitat openness were more important than protected area status for predicting vulture use.Main conclusionsThrough combining complex analyses, we identified results which simple statistical analyses could not offer. Hidden Markov models and point process models are complementary and can be used to define specific behaviours and associated resource selection. These results provide insight into how animals use their habitat explicitly rather than describing where they spend most of their time. This adds to the growing evidence that although National Parks are important, the management of surrounding areas must be included in conservation efforts.

Pairwise interaction Markov model for 3D epidermal nerve fibre endings.

In this paper, the spatial arrangement and possible interactions between epidermal nerve fibre endings are investigated and modelled by using confocal microscopy data. We are especially interested in possible differences between patterns from healthy volunteers and patients suffering from mild diabetic neuropathy. The locations of the points, where nerves enter the epidermis, the first branching points and the points where the nerve fibres terminate, are regarded as realizations of spatial point processes. We propose an anisotropic point process model for the locations of the nerve fibre endings in three dimensions, where the points interact in cylindrical regions. First, the locations of end points in are modelled as clusters around the branching points and then, the model is extended to three dimensions using a pairwise interaction Markov field model with cylindrical neighbourhood for the z-coordinates conditioned on the planar locations of the points. We fit the model to samples taken from healthy subjects and subjects suffering from diabetic neuropathy. In both groups, after a hardcore radius, there is some attraction between the end points. However, the range and strength of attraction are not the same in the two groups. Performance of the model is evaluated by using a cylindrical version of Ripley's K function due to the anisotropic nature of the data. Our findings suggest that the proposed model is able to capture the 3D spatial structure of the endpoints.

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

Mutually Exciting Point Process Graphs for Modeling Dynamic Networks

A new class of models for dynamic networks is proposed, called mutually exciting point process graphs (MEG). MEG is a scalable network-wide statistical model for point processes with dyadic marks, which can be used for anomaly detection when assessing the significance of future events, including previously unobserved connections between nodes. The model combines mutually exciting point processes to estimate dependencies between events and latent space models to infer relationships between the nodes. The intensity functions for each network edge are characterized exclusively by node-specific parameters, which allows information to be shared across the network. This construction enables estimation of intensities even for unobserved edges, which is particularly important in real world applications, such as computer networks arising in cyber-security. A recursive form of the log-likelihood function for MEG is obtained, which is used to derive fast inferential procedures via modern gradient ascent algorithms. An alternative EM algorithm is also derived. The model and algorithms are tested on simulated graphs and real world datasets, demonstrating excellent performance. Supplementary materials for this article are available online.

Spatial point pattern analysis of pine wilt disease occurrence and its influence factors

Pine wilt disease has caused huge losses in ecological and economic values in China, especially in the southern parts. Analyzing the spatial distribution of pine wilt disease and quantifying the impact of environmental factors on its occurrence were of great significance for its prevention and control. In this study, we examined the spatial pattern of pine wilt disease occurrence and its response to environmental variables in Nankang District, Ganzhou, Jiangxi Province, using kernel-smoothing density, Ripley's K function, and point process model. The results showed that the occurrence of pine wilt disease in the study region was not randomly distributed, but was obviously clustered at some areas. Terrain, vegetation, and human activity were the main factors affecting the heterogeneous distribution of pine wilt disease. Spatial point pattern analysis showed that altitude, slope, distance to the nearest road, road density, distance to nearest settlement, canopy closure, and vegetation type had significant effects on the occurrence of pine wilt disease. In addition to strengthening the control of disease transmission caused by human activities, we should also consider the effects of terrain and vegetation types for early warning and monitoring in forest disease management.

Estimation of forest stand characteristics using individual tree detection, stochastic geometry and a sequential spatial point process model

Airborne Laser Scanning (ALS) results in point-wise measurements of canopy height, which can further be used for Individual Tree Detection (ITD). However, ITD cannot find all trees because small trees can hide below larger tree crowns. Here we discuss methods where the plot totals and means of tree-level characteristics are estimated in such context. The starting point is a previously presented Horvitz–Thompson-like (HT-like) estimator, where the detectability is based on the larger tree crowns and a tuning parameter α that models the detection condition. We propose a new method which is based on modeling the spatial pattern of hidden tree locations using a sequential spatial point process model, with a tuning parameter θ. We also explore whether the variability of the tuning parameters α and θ can be predicted using ALS features to improve the predictions. The accuracy of stand density, dominant height and mean height is used as comparison criteria in a cross-validation procedure. The HT-like estimator with empirically estimated tuning parameter α performed the best. The overall performance of the new method was comparable. The new method was computationally less demanding, which makes it attractive for practical use.

Disordered Complex Networks: Energy Optimal Lattices and Persistent Homology

Disordered complex networks are of fundamental interest in statistical physics, and they have attracted recent interest as stochastic models for information transmission over wireless networks. While mathematically tractable, a network based on the regulation Poisson point process model offers challenges vis-a-vis network efficiency. Strongly correlated alternatives, such as networks based on random matrix spectra (the Ginibre network), on the other hand offer formidable challenges in terms of tractability and robustness issues. In this work, we demonstrate that network models based on random perturbations of Euclidean lattices <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">interpolate</i> between Poisson and rigidly structured networks, and allow us to achieve the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">best of both worlds</i> : significantly improve upon the Poisson model in terms of network efficacy measured by the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Signal to Interference plus Noise Ratio</i> (abbrv. SINR) and the related concept of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coverage probabilities</i> , at the same time retaining a considerable measure of mathematical and computational simplicity and robustness to erasure and noise. We investigate the optimal choice of the base lattice in this model, connecting it to the celebrated problem optimality of Euclidean lattices with respect to the Epstein Zeta function, which is in turn related to notions of lattice energy. This leads us to the choice of the triangular lattice in 2D and face centered cubic lattice in 3D, whose Gaussian perturbations we consider. We provide theoretical analysis and empirical investigations to demonstrate that the coverage probability decreases with increasing strength of perturbation, eventually converging to that of the Poisson network. In the regime of low disorder, our studies suggest an approximate statistical behaviour of the coverage function near a base station as a log-normal distribution with parameters depending on the Epstein Zeta function of the lattice, and related approximate dependencies for a power-law constant that governs the network coverage probability at large thresholds. In 2D, we determine the disorder strength at which the perturbed triangular lattice (abbrv. PTL) and the Ginibre networks are the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closest</i> measured by comparing their network topologies via a comparison of their <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Persistence Diagrams</i> in the total variation as well as the symmetrized nearest neighbour distances. We demonstrate that, at this very same disorder, the PTL and the Ginibre networks exhibit very similar coverage probability distributions, with the PTL performing at least as well as the Ginibre. Thus, the PTL network at this disorder strength can be taken to be an effective substitute for the Ginibre network model, while at the same time offering the advantages of greater tractability both from theoretical and empirical perspectives.

Spike prediction on primary motor cortex from medial prefrontal cortex during task learning

Objectives. Brain–machine interfaces (BMIs) aim to help people with motor disabilities by interpreting brain signals into motor intentions using advanced signal processing methods. Currently, BMI users require intensive training to perform a pre-defined task, not to mention learning a new task. Thus, it is essential to understand neural information pathways among the cortical areas in task learning to provide principles for designing BMIs with learning abilities. We propose to investigate the relationship between the medial prefrontal cortex (mPFC) and primary motor cortex (M1), which are actively involved in motor control and task learning, and show how information is conveyed in spikes between the two regions on a single-trial basis by computational models. Approach. We are interested in modeling the functional relationship between mPFC and M1 activities during task learning. Six Sprague Dawley rats were trained to learn a new behavioral task. Neural spike data was recorded from mPFC and M1 during learning. We then implement the generalized linear model, the second-order generalized Laguerre–Volterra model, and the staged point-process model to predict M1 spikes from mPFC spikes across multiple days during task learning. The prediction performance is compared across different models or learning stages to reveal the relationship between mPFC and M1 spike activities. Main results. We find that M1 neural spikes can be well predicted from mPFC spikes on the single-trial level, which indicates a highly correlated relationship between mPFC and M1 activities during task learning. By comparing the performance across models, we find that models with higher nonlinear capacity perform significantly better than linear models. This indicates that predicting M1 activity from mPFC activity requires the model to consider higher-order nonlinear interactions beyond pairwise interactions. We also find that the correlation coefficient between the mPFC and M1 spikes increases during task learning. The spike prediction models perform the best when the subjects become well trained on the new task compared with the early and middle stages. The results suggest that the co-activation between mPFC and M1 activities evolves during task learning, and becomes stronger as subjects become well trained. Significance. This study demonstrates that the dynamic patterns of M1 spikes can be predicted from mPFC spikes during task learning, and this will further help in the design of adaptive BMI decoders for task learning.

Network Hawkes Process Models for Exploring Latent Hierarchy in Social Animal Interactions

AbstractGroup-based social dominance hierarchies are of essential interest in understanding social structure (DeDeo &amp; Hobson in, Proceedings of the National Academy of Sciences 118(21), 2021). Recent animal behaviour research studies can record aggressive interactions observed over time. Models that can explore the underlying hierarchy from the observed temporal dynamics in behaviours are therefore crucial. Traditional ranking methods aggregate interactions across time into win/loss counts, equalizing dynamic interactions with the underlying hierarchy. Although these models have gleaned important behavioural insights from such data, they are limited in addressing many important questions that remain unresolved. In this paper, we take advantage of the observed interactions' timestamps, proposing a series of network point process models with latent ranks. We carefully design these models to incorporate important theories on animal behaviour that account for dynamic patterns observed in the interaction data, including the winner effect, bursting and pair-flip phenomena. Through iteratively constructing and evaluating these models we arrive at the final cohort Markov-modulated Hawkes process (C-MMHP), which best characterizes all aforementioned patterns observed in interaction data. As such, inference on our model components can be readily interpreted in terms of theories on animal behaviours. The probabilistic nature of our model allows us to estimate the uncertainty in our ranking. In particular, our model is able to provide insights into the distribution of power within the hierarchy which forms and the strength of the established hierarchy. We compare all models using simulated and real data. Using statistically developed diagnostic perspectives, we demonstrate that the C-MMHP model outperforms other methods, capturing relevant latent ranking structures that lead to meaningful predictions for real data.

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.

Asymptotic Dependence Modelling of the BRICS Stock Markets

With the use of empirical data, this paper focuses on solving financial and investment issues involving extremal dependence of 10 pairwise combinations of the 5 BRICS (Brazil, Russia, India, China, and South Africa) stock markets. Daily closing equity indices from 5 January 2010 to 6 August 2018 are used in the study. Unlike previous literature, we use bivariate point process and conditional multivariate extreme value models to investigate the extremal dependence of the stock market returns. However, it is observed that the point process was able to model many more extreme observations or exceedances that contribute to the likelihood estimation. It gives more information than the threshold excess method of the CMEV model. This study shows varying levels of low extremal dependence structure whose outcomes are highly beneficial to investors, portfolio managers and other market participants interested in maximising investment returns and financial gains.

Unified Analysis of Coordinated Multipoint Transmissions in mmWave Cellular Networks

This article performs a unified analysis of three coordinated multipoint (CoMP) transmission strategies in the downlink of mmWave cellular networks, including the fixed-number base station (BS) cooperation (FNC), the fixed-region BS cooperation (FRC), and the interference-aware BS cooperation (IAC). We first develop a comprehensive framework for CoMP operation in cellular networks, and investigate the network performance under a Poisson point process (PPP) model together with mmWave spectrum. To show what fraction of users in the network achieve target reliability for a given signal to interference-plus-noise ratio (SINR)/signal-to-interference ratio (SIR), we derive the SINR/SIR meta distributions, and further obtain the coverage probability as well as mean local delay for the three cooperation strategies. A pivotal intermediate step to compute the performance metrics is the derivation of joint distributions of distances between a typical user and cooperative BSs. Our analysis demonstrates that parameters of blockage have a significant influence on the network performance for the three CoMP schemes. We find that the FRC scheme makes more users achieve the given link reliability for the scenario with a low density of BSs, while the IAC scheme provides better performance for the network with a high density of BSs. Moreover, the optimal CoMP scheme can be approximately selected by considering the nearest distance from the serving BS to user and the radius of the approximate line-of-sight (LoS) region in the cellular networks.

Modeling Neural Connectivity in a Point-Process Analogue of Kalman Filter.

A neural encoding model describes how single neuron tunes to external stimuli as well as its connectivity with other neurons. The connectivity illustrates the neuronal interaction within populations in response to the shared latent brain states. Understanding these interactions is crucial to computationally predict the neural activity, which elucidates the neural encoding mechanism A computational analysis on the neural connectivity also facilitates developing more point process decoding model to interpret movement state from neural spike observations for brain machine interfaces (BMI). Most of the previous point process models only consider single neural tuning property and assumes conditional independence among multiple neurons. The connectivity among neurons is not considered in such a Bayesian approach to derive the state. In this work, we propose a point-process analogue of Kalman Filter to model the neural connectivity in a closed-form Bayesian filter. Neural connectivity corrects the posterior of the state given the multi-dimension observation, and a Gaussian distribution is used to approximate the updated posterior distribution. We validate the proposed method on simulation data and compared with traditional point process filtering with conditional independent assumption. The result shows that our method models the neural connectivity information and the single neuronal tuning property at the same time and achieves a better performance of the state decoding. Clinical Relevance - This paper proposes a closed-form derivation of a point process filter based on Gaussian approximations. It can model both single neuronal tuning property and the neural connectivity, which is potential to understanding the neural connectivity computationally.

Estimating a Non-parametric Memory Kernel for Mutually Exciting Point Processes

Abstract Self- and cross-excitation in point processes are commonly captured in the financial econometrics literature using a multivariate exponential memory kernel. In this article, the exponential assumption is relaxed and the resultant non-parametric memory kernel is estimated by a method based on second-order cumulants. The estimator is shown to be consistent and asymptotically normally distributed and performs well under simulation. An empirical application based on 10 international stock indices is presented. Two different indices of contagion between markets are constructed from the point process models in order to examine interconnection over time. A conclusion which emerges from these results is the assumption that a parametric kernel may be too restrictive as the application reveals interesting features, and in some cases substantial differences, between the exponential and non-parametric kernels.