Point Process Model Research Articles

A Bayesian hierarchical point process model for epidermal nerve fiber patterns

We introduce the Thomas process in a Bayesian hierarchical setting as a model for point pattern data with a nested structure. This model is applied to a nerve fiber data set which consists of several point patterns of nerve entry points from 47 subjects divided into 3 groups, where the grouping is based on the diagnosed severity of a certain nerve disorder. The modeling assumption is that each point pattern is a realization of a Thomas process, with parameter values specific to the subject. These parameter values are in turn assumed to come from distributions that depend on which group the subject belongs to. To fit the model, we construct an MCMC algorithm, which is evaluated in a simulation study. The results of the simulation study indicate that the group level mean of each parameter is well estimated, but that the estimation of the between subject variance is more challenging. When fitting the model to the nerve fiber data, we find that the structure within clusters appears to be the same in all groups, but that the number of clusters decreases with the progression of the nerve disorder.

Lateralization of directional brain-heart information transfer during visual emotional elicitation.

Previous studies have characterized the physiological interactions between central nervous system (brain) and peripheral cardiovascular system (heart) during affective elicitation in healthy subjects; however, questions related to the directionality of this functional interplay have been gaining less attention from the scientific community. Here, we explore brain-heart interactions during visual emotional elicitation in healthy subjects using measures of Granger causality (GC), a widely used descriptor of causal influences between two dynamical systems. The proposed approach inferences causality between instantaneous cardiovagal dynamics estimated from inhomogeneous point-process models of the heartbeat and high-density electroencephalogram (EEG) dynamics in 22 healthy subjects who underwent pleasant/unpleasant affective elicitation by watching pictures from the International Affective Picture System database. Particularly, we calculated the GC indexes between the EEG spectrogram in the canonical θ-, α-, β-, and γ-bands and both the instantaneous mean heart rate and its continuous parasympathetic modulations (i.e., the instantaneous HF power). Thus we looked for significant statistical differences among GC values estimated during the resting state, neutral elicitation, and pleasant/unpleasant arousing elicitation. As compared with resting state, coupling strength increases significantly in the left hemisphere during positive stimuli and in the right hemisphere during negative stimuli. Our results further reveal a correlation between emotional valence and lateralization of the dynamical information transfer going from brain-to-heart, mainly localized in the prefrontal, somatosensory, and posterior cortexes, and of the information transfer from heart-to-brain, mainly reflected into the fronto-parietal cortex oscillations in the γ-band (30-45 Hz).

Interference-Aware Channel Assignment Algorithm in D2D overlaying Cellular Networks

Device-to-Device (D2D) communications can provide proximity based services in the future 5G cellular networks. It allows short range communication in a limited area with the advantages of power saving, high data rate and traffic offloading. However, D2D communications may reuse the licensed channels with cellular communications and potentially result in critical interferences to nearby devices. To control the interference and improve network throughput in overlaid D2D cellular networks, a novel channel assignment approach is proposed in this paper. First, we characterize the performance of devices by using Poisson point process model. Then, we convert the throughput maximization problem into an optimal spectrum allocation problem with signal to interference plus noise ratio constraints and solve it, i.e., assigning appropriate fractions of channels to cellular communications and D2D communications. In order to mitigate the interferences between D2D devices, a cluster-based multi-channel assignment algorithm is proposed. The algorithm first cluster D2D communications into clusters to reduce the problem scale. After that, a multi-channel assignment algorithm is proposed to mitigate critical interferences among nearby devices for each D2D cluster individually. The simulation analysis conforms that the proposed algorithm can greatly increase system throughput.

Global multivariate point pattern models for rain type occurrence

We seek statistical methods to study the occurrence of multiple rain types observed by satellite on a global scale. The main scientific interests are to relate rainfall occurrence with various atmospheric state variables and to study the dependence between the occurrences of multiple types of rainfall (e.g. short-lived and intense vs. long-lived and weak; the heights of the rain clouds are also considered). Commonly in point process model literature, the spatial domain is assumed to be a small, and thus planar domain. We consider the log-Gaussian Cox Process (LGCP) models on the surface of a sphere and take advantage of cross-covariance models for spatial processes on a global scale to model the stochastic intensity function of the LGCP models. We present analysis results for rainfall observations from the TRMM satellite and atmospheric state variables from MERRA-2 reanalysis data over the tropical Eastern and Western Pacific Ocean, as well as over the entire tropical and subtropical ocean regions. Statistical inference is done through Monte Carlo likelihood approximation for LGCP models. We employ covariance approximation to deal with massive data.

Spatial Analysis of a Cat-Borne Disease Reveals That Soil pH and Clay Content Are Risk Factors for Sarcocystosis in Sheep.

Cat-borne parasites and their associated diseases have substantial impacts on human, livestock, and wildlife health worldwide. Despite this, large and detailed datasets that allow researchers to study broad-scale trends in the ecology of cat-borne diseases are either difficult to obtain or non-existent. One condition that is easily detected at slaughter is macroscopic sarcocystosis, a cat-borne parasitosis of sheep (Ovis aries). We conducted a cross-sectional study to describe the geographic distribution of sarcocystosis in sheep throughout South Australia and investigate ecosystem characteristics associated with the presence of disease. Data were obtained from two slaughterhouses which processed 3,865,608 sheep from 4,204 farms across 385,468 km2 of South Australia's land mass for the period 2007–2017. A Poisson point process model was developed to quantify environmental characteristics associated with higher densities of sarcocystosis-positive farms. Sarcocystosis was highly clustered on a large island off of the Australian coast and the density of sarcocystosis-positive farms increased in areas of low soil pH (intensity ratio: 0.86, 95% CI: 0.78, 0.95) and high clay content. We hypothesize that region was confounded by, and predominately acted as a proxy for, cat density. Our results have broader implications regarding the health, welfare, economic, and conservation impacts of other cat-borne parasitosis, such as toxoplasmosis.

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.

NARROW GAP DETECTION IN MICROSCOPE IMAGES USING MARKED POINT PROCESS MODELING.

Differentiating objects separated by narrow gaps is a challenging and important task in analyzing microscopic images. These small separations provide useful information for applications that require detailed boundary information and/or an accurate particle count. We present a new approach to the modeling of these gaps based on a marked point process(MPP) framework. We propose to model narrow gaps as geometric structures called channels, and define Gibbs energies for these models. The Reversible-jump Markov chain Monte Carlo(RJMCMC) algorithm embedded with simulated annealing is used as an optimization method, and the switching kernel in an RJMCMC is newly designed to speed up the algorithm. In this paper, we also propose a method to exploit a detected channel configuration to reduce bridging channel defects in conventional segmentation algorithms. Experimental results demonstrate that the proposed channel modeling methods are successful in detecting gaps between closely adjacent objects. The results also show that the proposed interaction parameter control method improves boundary precision in the segmentation of microscopic images.

Structured Space-Sphere Point Processes and K-Functions

This paper concerns space-sphere point processes, that is, point processes on the product space of $\mathbb {R}^{d}$ (the d-dimensional Euclidean space) and $\mathbb {S}^{k}$ (the k-dimensional sphere). We consider specific classes of models for space-sphere point processes, which are adaptations of existing models for either spherical or spatial point processes. For model checking or fitting, we present the space-sphere K-function which is a natural extension of the inhomogeneous K-function for point processes on $\mathbb {R}^{d}$ to the case of space-sphere point processes. Under the assumption that the intensity and pair correlation function both have a certain separable structure, the space-sphere K-function is shown to be proportional to the product of the inhomogeneous spatial and spherical K-functions. For the presented space-sphere point process models, we discuss cases where such a separable structure can be obtained. The usefulness of the space-sphere K-function is illustrated for real and simulated datasets with varying dimensions d and k.

Space–time inhomogeneous background intensity estimators for semi-parametric space–time self-exciting point process models

Histogram maximum likelihood estimators of semi-parametric space–time self-exciting point process models via expectation–maximization algorithm can be biased when the background process is inhomogeneous. We explore an alternative estimation method based on the variable bandwidth kernel density estimation (KDE) and EM algorithm. The proposed estimation method involves expanding the semi-parametric models by incorporating an inhomogeneous background process in space and time and applying the variable bandwidth KDE to estimate the background intensity function. Using an example, we show how the variable bandwidth KDE can be estimated this way. Two simulation examples based on residual analysis are designed to evaluate and validate the ability of our methods to recover the background intensity function and parametric triggering intensity function.

SIR Meta Distribution of $K$ -Tier Downlink Heterogeneous Cellular Networks With Cell Range Expansion

Heterogeneous cellular networks (HCNs) constitute a necessary step in the evolution of cellular networks. In this paper, we apply the signal-to-interference ratio (SIR) meta distribution framework for a refined SIR performance analysis of HCNs, focusing on K-tier heterogeneous cellular networks based on the homogeneous independent Poisson point process (HIP) model, with range expansion bias (offloading bias) in each tier. Expressions for the b-th moment of the conditional success probability for both the entire network and each tier are derived, based on which the exact meta distributions and the beta approximations are evaluated and compared. Key performance metrics including the mean success probability, the variance of the conditional success probability, the mean local delay and the asymptotic SIR gains of each tier are obtained. The results show that the biases are detrimental to the overall mean success probability of the whole network and that the b-th moment curve (versus the SIR threshold) of the conditional success probability of each tier can be excellently approximated by the horizontal shifted versions of the first moment curve of the single-tier PPP network. We also provide lower bounds for the region of the active probabilities of the base stations to keep the mean local delay of each tier finite.

Asymptotic equivalence of fixed-size and varying-size determinantal point processes

Determinantal Point Processes (DPPs) are popular models for point processes with repulsion. They appear in numerous contexts, from physics to graph theory, and display appealing theoretical properties. On the more practical side of things, since DPPs tend to select sets of points that are some distance apart (repulsion), they have been advocated as a way of producing random subsets with high diversity. DPPs come in two variants: fixed-size and varying-size. A sample from a varying-size DPP is a subset of random cardinality, while in fixed-size “$k$-DPPs” the cardinality is fixed. The latter makes more sense in many applications, but unfortunately their computational properties are less attractive, since, among other things, inclusion probabilities are harder to compute. In this work, we show that as the size of the ground set grows, $k$-DPPs and DPPs become equivalent, in the sense that fixed-order inclusion probabilities converge. As a by-product, we obtain saddlepoint formulas for inclusion probabilities in $k$-DPPs. These turn out to be extremely accurate, and suffer less from numerical difficulties than exact methods do. Our results also suggest that $k$-DPPs and DPPs also have equivalent maximum likelihood estimators. Finally, we obtain results on asymptotic approximations of elementary symmetric polynomials which may be of independent interest.

Meta Distribution of SIR in Large-Scale Uplink and Downlink NOMA Networks

We develop an analytical framework to derive the meta distribution and moments of the conditional success probability (CSP), which is defined as success probability for a given realization of the transmitters, in large-scale co-channel uplink and downlink non-orthogonal multiple access (NOMA) networks with one NOMA cluster per cell. The moments of CSP translate to various network performance metrics such as the standard success or signal-to-interference ratio (SIR) coverage probability (which is the 1-st moment), the mean local delay (which is the −1st moment in a static network setting), and the meta distribution (which is the complementary cumulative distribution function of the success or SIR coverage probability and can be approximated by using the 1st and 2nd moments). For the uplink NOMA network, to make the framework tractable, we propose two point process models for the spatial locations of the inter-cell interferers by utilizing the base station (BS)/user pair correlation function. We validate the proposed models by comparing the second moment measure of each model with that of the actual point process for the inter-cluster (or inter-cell) interferers obtained via simulations. For downlink NOMA, we derive closed-form solutions for the moments of the CSP, success (or coverage) probability, mean local delay, and meta distribution for the users. As an application of the developed analytical framework, we use the closed-form expressions to optimize the power allocations for downlink NOMA users in order to maximize the success probability of a given NOMA user with and without latency constraints. Closed-form optimal solutions for the transmit powers are obtained for two-user NOMA scenario. We note that maximizing the success probability with latency constraints can significantly impact the optimal power solutions for low SIR thresholds and favor orthogonal multiple access.

Estimating Multiscale Direct Causality Graphs in Neural Spike-Field Networks

Neural representations span various spatiotemporal scales of brain activity, from the spiking activity of single neurons to field activity measuring large-scale networks. The simultaneous analyses of spikes and fields to uncover causal interactions in multiscale networks could help understand neural mechanisms. However, assessing causality within spike-field networks is challenging as spikes are binary-valued with a fast time-scale while fields are continuous-valued with slower time-scales. Current causality measures are largely not applicable to mixed discrete-continuous network activity. Here, in this paper, we develop a novel multiscale causality estimation algorithm for spike-field networks. We construct a likelihood function comprised of point process models for spikes and linear Gaussian models for fields. For spikes, firing rates are modeled as a function of the history of both field signals and binary spike events within the network. For fields, to make their linear models consistent with biophysical findings, we use the history of field signals and the history of the latent log-firing rates of neurons as predictors. To resolve the challenge of estimating the network model parameters in the presence of latent firing rates, we develop a sequential maximum-likelihood parameter estimation procedure that extends to large networks. Once models are estimated, we compute directed information as our measure of multiscale causality and devise two statistical tests to assess its significance. Using extensive simulations, we show that the algorithm can accurately reconstruct the true causality graphs of random spike-field networks. Moreover, the algorithm is robust to the number of connections, connection strengths, or exact topology of the network. This multiscale causality estimation algorithm has important implications for studying neural mechanisms and for future neurotechnology design.

Marked point process models for the admissions of heart failure patients

The aim of this paper is to model the stochastic process of hospitalizations with marked point processes (MPPs). We examine the longitudinal data set including the admissions of heart failure patients to Lombardia hospitals on a follow‐up period of 6 years since January 1, 2006. We analyze four separate groups of patients, which we call heart failure groups, according to their diagnoses‐codes contained in the SDO (hospital discharge form) of their first hospitalizations. The statistical model links the temporal trend of hospitalization (the ground process) with the length of stay (the mark) at each event. Instead of framing our application in the more theoretical context of the counting measures and processes, we make use of the conditional intensity function, a parametric approach which leads us to deal with Hawkes processes. Hypotheses are made on the mark concerning its distribution as well as its independence or dependence with the ground process. Independence is better to model and give us significant results while dependence is harder to be dealt with due to computational and modeling issues. Finally, we provide a general framework for modeling longitudinal data with a MPP as a method for statistical inference and suggest a specific model for our topic, validating it through a goodness of fit technique.

Understanding species distribution in dynamic populations: a new approach using spatio‐temporal point process models

Understanding and predicting a species’ distribution across a landscape is of central importance in ecology, biogeography and conservation biology. However, it presents daunting challenges when populations are highly dynamic (i.e. increasing or decreasing their ranges), particularly for small populations where information about ecology and life history traits is lacking. Currently, many modelling approaches fail to distinguish whether a site is unoccupied because the available habitat is unsuitable or because a species expanding its range has not arrived at the site yet. As a result, habitat that is indeed suitable may appear unsuitable. To overcome some of these limitations, we use a statistical modelling approach based on spatio‐temporal log‐Gaussian Cox processes. These model the spatial distribution of the species across available habitat and how this distribution changes over time, relative to covariates. In addition, the model explicitly accounts for spatio‐temporal dynamics that are unaccounted for by covariates through a spatio‐temporal stochastic process. We illustrate the approach by predicting the distribution of a recently established population of Eurasian cranes Grus grus in England, UK, and estimate the effect of a reintroduction in the range expansion of the population. Our models show that wetland extent and perimeter‐to‐area ratio have a positive and negative effect, respectively, in crane colonisation probability. Moreover, we find that cranes are more likely to colonise areas near already occupied wetlands and that the colonisation process is progressing at a low rate. Finally, the reintroduction of cranes in SW England can be considered a human‐assisted long‐distance dispersal event that has increased the dispersal potential of the species along a longitudinal axis in S England. Spatio‐temporal log‐Gaussian Cox process models offer an excellent opportunity for the study of species where information on life history traits is lacking, since these are represented through the spatio‐temporal dynamics reflected in the model.

A spatio-temporal point process model for particle growth

AbstractA spatio-temporal model of particle or star growth is defined, whereby new unit masses arrive sequentially in discrete time. These unit masses are referred to as candidate stars, which tend to arrive in mass-dense regions and then either form a new star or are absorbed by some neighbouring star of high mass. We analyse the system as time increases, and derive the asymptotic growth rate of the number of stars as well as the size of a randomly chosen star. We also prove that the size-biased mass distribution converges to a Poisson–Dirichlet distribution. This is achieved by embedding our model into a continuous-time Markov process, so that new stars arrive according to a marked Poisson process, with locations as marks, whereas existing stars grow as independent Yule processes. Our approach can be interpreted as a Hoppe-type urn scheme with a spatial structure. We discuss its relevance for and connection to models of population genetics, particle aggregation, image segmentation, epidemic spread, and random graphs with preferential attachment.

Modeling spatial overdispersion via the generalized Waring point process

AbstractModeling spatial overdispersion requires point process models with finite‐dimensional distributions that are overdisperse relative to the Poisson distribution. Fitting such models usually heavily relies on the properties of stationarity, ergodicity, and orderliness. In addition, although processes based on negative binomial finite‐dimensional distributions have been widely considered, they typically fail to simultaneously satisfy the three required properties for fitting. Indeed, it has been conjectured by Diggle and Milne that no negative binomial model can satisfy all three properties. In light of this, we change perspective and construct a new process based on a different overdisperse count model, namely, the generalized Waring (GW) distribution. While comparably tractable and flexible to negative binomial processes, the GW process is shown to possess all required properties and additionally span the negative binomial and Poisson processes as limiting cases. In this sense, the GW process provides an approximate resolution to the conundrum highlighted by Diggle and Milne.

Spatiotemporal distribution dynamics of elephants in response to density, rainfall, rivers and fire in Kruger National Park, South Africa

AbstractAimAfrican elephants are ecosystem engineers. As such, their long‐term patterns of distribution and abundance (i.e., space‐use intensity) will influence ecosystem structure and function. We elucidate these patterns for bull versus herd groups, by analysing the spatiotemporal dynamics of an increasing elephant population in relation to key ecological drivers: rainfall, distance to major rivers and time since last fire. Significant changes to the long‐term patterns of elephant density and group‐type probabilities are identified and explained.LocationKruger National Park, South Africa.MethodsUsing almost three decades of census records (1985–2012), we applied Multiple Point Process Models to assess the influence of rainfall, rivers and fire in shaping elephant space‐use. Significant changes to the long‐term patterns of elephant density and group type were also identified using kernel density estimates and the spatially varying probability of encountering either bull or herd group.ResultsBull and herd groups are no longer clearly segregated as available empty space becomes more limited. Bull and herd groups have dichotomous resource selection functions, in that bulls concentrate in areas receiving lower rainfall but more frequent fires while herds concentrate in higher rainfall areas experiencing less frequent fires. Both bull and herd groups concentrate closer to major rivers, emphasizing rivers as important spatial drivers. Overall, densities increased most significantly closer to rivers and in areas experiencing fewer fires. Fire was also a strong agent of group‐type change, as the probability of finding bulls, contrary to herds, significantly increased as fire return periods shortened.Main conclusionsElephant distribution and abundance patterns have homogenized in response to increased space limitations, with group‐specific, fire‐driven distribution patterns emerging overtime. Results herein should be used to help manage elephant space‐use through the establishment of possible refuge areas and the development of more empirical research into elephant impacts in future.

Disentangling the functional trait correlates of spatial aggregation in tropical forest trees.

Environmental filtering and dispersal limitation can both maintain diversity in plant communities by aggregating conspecifics, but parsing the contribution of each process has proven difficult empirically. Here, we assess the contribution of filtering and dispersal limitation to the spatial aggregation patterns of 456 tree species in a hyperdiverse Amazonian forest and find distinct functional trait correlates of interspecific variation in these processes. Spatial point process model analysis revealed that both mechanisms are important drivers of intraspecific aggregation for the majority of species. Leaf drought tolerance was correlated with species topographic distributions in this aseasonal rainforest, showing that future increases in drought severity could significantly impact community structure. In addition, seed mass was associated with the spatial scale and density of dispersal-related aggregation. Taken together, these results suggest environmental filtering and dispersal limitation act in concert to influence the spatial and functional structure of diverse forest communities.

Predicting the Impact of Climate Change on Severe Wintertime Particulate Pollution Events in Beijing Using Extreme Value Theory

AbstractWe use extreme value theory to develop point process statistical models relating the probability of extreme winter particulate pollution events in Beijing (“winter haze”) to local meteorological variables. The models are trained with the 2009–2017 record of fine particulate matter concentrations (PM2.5) from the U.S. embassy. We find that 850‐hPa meridional wind velocity (V850) and relative humidity successfully predict the probability for 24‐hr average PM2.5 to exceed 300 μg/m3 (95th percentile of the frequency distribution) as well as higher thresholds. We apply the point process models to mid‐21st century climate projections from the Coupled Model Intercomparison Project Phase 5 model ensemble under two radiative forcing scenarios (RCP8.5 and RCP4.5). We conclude that 21st century climate change alone is unlikely to increase the frequency of severe PM2.5 pollution events (PM2.5 > 300 μg/m3) in Beijing and is more likely to marginally decrease the probability of such events.