Search

We propose a semi-parametric spatio-temporal Hawkes process with periodic components to model the occurrence of car accidents in a given spatio-temporal window. The overall intensity is split into the sum of a background component capturing the spatio-temporal varying intensity and an excitation component accounting for the possible triggering effect between events. The spatial background is estimated and evaluated on the road network, allowing the derivation of accurate risk maps of road accidents. We constrain the spatio-temporal excitation to preserve an isotropic behaviour in space, and we generalize it to account for the effect of covariates. The estimation is pursued by maximizing the expected complete data log-likelihood using a tailored version of the stochastic-reconstruction algorithm that adopts ad hoc boundary correction strategies. An original application analyses the car accidents that occurred on the Rome road network in the years 2019, 2020, and 2021. Results highlight that car accidents of different types exhibit varying degrees of excitation, ranging from no triggering to a 10% chance of triggering further events. [ABSTRACT FROM AUTHOR] more...

Since the seminal work of Kolmogorov, probability theory has been based on measure theory, where the central components are so-called probability measures, defined as measures with total mass equal to 1. In Kolmogorov's theory, a probability measure is used to model an experiment with a single outcome that will belong to exactly one out of several disjoint sets. In this paper, we present a different basic model where an experiment results in a multiset, i.e., for each of the disjoint sets we obtain the number of observations in the set. This new framework is consistent with Kolmogorov's theory, but the theory focuses on expected values rather than probabilities. We present examples from testing goodness-of-fit, Bayesian statistics, and quantum theory, where the shifted focus gives new insight or better performance. We also provide several new theorems that address some problems related to the change in focus. [ABSTRACT FROM AUTHOR] more...

AbstractLongitudinal networks consist of sequences of temporal edges among multiple nodes, where the temporal edges are observed in real-time. They have become ubiquitous with the rise of online social platforms and e-commerce, but largely under-investigated in the literature. In this paper, we propose an efficient estimation framework for longitudinal networks, leveraging strengths of adaptive network merging, tensor decomposition, and point processes. It merges neighboring sparse networks so as to enlarge the number of observed edges and reduce estimation variance, whereas the estimation bias introduced by network merging is controlled by exploiting local temporal structures for adaptive network neighborhood. A projected gradient descent algorithm is proposed to facilitate estimation, where the upper bound of the estimation error in each iteration is established. A thorough analysis is conducted to quantify the asymptotic behavior of the proposed method, which shows that it can significantly reduce the estimation error and also provides a guideline for network merging under various scenarios. We further demonstrate the advantage of the proposed method through extensive numerical experiments on synthetic datasets and a militarized interstate dispute dataset. [ABSTRACT FROM AUTHOR] more...

Simple Summary: Clear cell renal cell carcinoma (ccRCC) is the most common type of kidney cancer, but predicting its behavior remains challenging using standard histopathologic examination. This study introduces a novel approach to predict ccRCC aggressiveness by analyzing the spatial distribution of tumor cells in H&E-stained images. The researchers found that spatial analysis outperformed traditional tumor grading in predicting metastasis, particularly for intermediate-grade tumors. They identified two distinct patient groups based on spatial characteristics, with one group showing greater spatial randomness and a higher association with metastasis. Furthermore, the study revealed a gene expression signature related to the extracellular matrix (matrisome) that correlated with the spatial patterns and aggressive tumor behavior. These findings suggest that analyzing the spatial distribution of ccRCC tumor cells could provide valuable insights into tumor behavior and metastatic potential, potentially improving prognostication and personalized treatment strategies for patients with ccRCC. Background/Objectives: Predicting the behavior of clear cell renal cell carcinoma (ccRCC) is challenging using standard-of-care histopathologic examination. Indeed, pathologic RCC tumor grading, based on nuclear morphology, performs poorly in predicting outcomes of patients with International Society of Urological Pathology/World Health Organization grade 2 and 3 tumors, which account for most ccRCCs. Methods: We applied spatial point process modeling of H&E-stained images of patients with grade 2 and grade 3 ccRCCs (n = 72) to find optimum separation into two groups. Results: One group was associated with greater spatial randomness and clinical metastasis (p < 0.01). Notably, spatial analysis outperformed standard pathologic grading in predicting clinical metastasis. Moreover, cell-to-cell interaction distances in the metastasis-associated group were significantly greater than those in the other patient group and were also greater than expected by the random distribution of cells. Differential gene expression between the two spatially defined groups of patients revealed a matrisome signature, consistent with the extracellular matrix's crucial role in tumor invasion. The top differentially expressed genes (with a fold change > 3) stratified a larger, multi-institutional cohort of 352 ccRCC patients from The Cancer Genome Atlas into groups with significant differences in survival and TNM disease stage. Conclusions: Our results suggest that the spatial distribution of ccRCC tumor cells can be extracted from H&E-stained images and that it is associated with metastasis and with extracellular matrix genes that are presumably driving these tumors' aggressive behavior. [ABSTRACT FROM AUTHOR] more...

AbstractEstimating the Hawkes process from a discretely observed sample path is challenging due to the intractability of the likelihood in such cases. To overcome this, we employ a state-space representation of the incomplete data problem and use the sequential Monte Carlo (SMC, aka particle filters) to approximate the likelihood function. The resulting estimator of the likelihood function is unbiased and, therefore, can be used along with the Metropolis-Hastings algorithm to construct Markov Chains to approximate the likelihood distribution and, more generally, the posterior distribution of model parameters. The performance of our methodology is assessed using simulation experiments and compared with other recently published methods. The proposed estimator exhibits a smaller mean square error compared to two benchmark estimators. Furthermore, an advantage of our method compared to existing methods is that confidence intervals for the parameters are readily computable. Finally, we apply the proposed estimator to the analysis of weekly count data on measles cases in Tokyo, Japan, and compare the results to one of the benchmark methods. The online supplementary materials contain a Julia package that implements our methodology, along with the technical proofs for two propositions. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR] more...

Shared landscapes in which humans and wildlife coexist, are increasingly recognized as integral to conservation. Fine‐scale data on the distribution and density of threatened wildlife are therefore critical to promote long‐term coexistence. Yet, the spatial complexity of habitat, anthropic threats and animal behaviour in shared landscapes challenges conventional survey techniques. For social wildlife in particular, the size of sub‐groups or clusters is likely to both vary in space and influence detectability, biasing density estimation and spatial prediction. Using the R package ‘inlabru', we develop a full‐likelihood joint log‐Gaussian Cox process to simultaneously perform spatial distance sampling and model a spatially varying cluster size distribution, which we condition upon detection probability to mitigate cluster‐size detection bias. We accommodate spatial dependencies by incorporating a non‐stationary Gaussian Markov random field, enabling the explicit inclusion of geographical barriers to wildlife dispersal. We demonstrate this model using 136 georeferenced detections of Campbell's monkey Cercopithecus campbelli clusters, collected with 398.56 km of line transects across a shared agroforest landscape mosaic (1067 km2) in Guinea‐Bissau. We assess a suite of anthropogenic and environmental spatial covariates, finding that normalized difference vegetation index (NDVI) and proximity to mangroves are both powerful spatial predictors of density. We captured strong spatial variation in cluster size, likely driven by fission–fusion in response to the complex distribution of resources and risk in the landscape. If left unaccounted for under existing approaches, such variation may bias density surface estimation. We estimate a population of 10 301 (95% CI [7606–14 104]) individuals and produce a fine‐scale predictive density map, revealing the importance of mangrove‐habitat interfaces for the conservation of this heavily hunted primate. This work demonstrates a powerful, widely applicable approach for monitoring socially flexible wildlife and informing evidence‐based conservation in complex, heterogeneous landscapes moving forward. [ABSTRACT FROM AUTHOR] more...

We consider Palm distributions arising in a Markov process with time homogeneous transitions which is jointly stationary with multiple point processes. Motivated by a BAR approach studied in the recent paper (Braverman et al. in the BAR approach for multi-class queueing networks with SBP service policies, 2023), we are interested in two problems; when this Markov process inherits the same Markov structure under the Palm distributions, and how the state changes at counting instants of the point processes can be handled to derive stationary equations when there are simultaneous counts and each of them influences the state changes. We affirmatively answer the first problem, and propose a framework for resolving the second problem, which is applicable to a general stationary process, which is not needed to be Markov. We also discuss how those results can be applied in deriving BAR's for the diffusion approximation of queueing models in heavy traffic. In particular, as their new application, the heavy traffic limit of the stationary distribution is derived for a single-server queue with a finite waiting room. [ABSTRACT FROM AUTHOR] more...

We introduce a class of proper scoring rules for evaluating spatial point process forecasts based on summary statistics. These scoring rules rely on Monte Carlo approximations of expectations and can therefore easily be evaluated for any point process model that can be simulated. In this regard, they are more flexible than the commonly used logarithmic score and other existing proper scores for point process predictions. The scoring rules allow for evaluating the calibration of a model to specific aspects of a point process, such as its spatial distribution or tendency toward clustering. Using simulations, we analyze the sensitivity of our scoring rules to different aspects of the forecasts and compare it to the logarithmic score. Applications to earthquake occurrences in northern California, United States and the spatial distribution of Pacific silver firs in Findley Lake Reserve in Washington highlight the usefulness of our scores for scientific model selection. [ABSTRACT FROM AUTHOR] more...

Several approaches to estimating the productivity function for a Hawkes point process with variable productivity are discussed, improved upon, and compared in terms of their root-mean-squared error and computational efficiency for various data sizes, and for binned as well as unbinned data. We find that for unbinned data, a regularized version of the analytic maximum likelihood estimator proposed by Schoenberg is the most accurate but is computationally burdensome. The unregularized version of the estimator is faster to compute but has lower accuracy, though both estimators outperform empirical or binned least squares estimators in terms of root-mean-squared error, especially when the mean productivity is 0.2 or greater. For binned data, binned least squares estimates are highly efficient both in terms of computation time and root-mean-squared error. An extension to estimating transmission time density is discussed, and an application to estimating the productivity of Covid-19 in the United States as a function of time from January 2020 to July 2022 is provided. [ABSTRACT FROM AUTHOR] more...

Aim: Accounting for biotic interactions in species distribution models is complicated by the fact that interactions occur at the individual‐level at unknown spatial scales. Standard approaches that ignore individual‐level interactions and focus on aggregate scales are subject to the modifiable aerial unit problem (MAUP) in which incorrect inferences may arise about the sign and magnitude of interspecific effects. Location: Global (simulation) and North Carolina, United States (case study). Taxon: None (simulation) and Aves (case study). Methods: We present a hierarchical species distribution model that includes a Markov point process in which the locations of individuals of one species are modelled as a function of both abiotic variables and the locations of individuals of another species. We applied the model to spatial capture‐recapture (SCR) data on two ecologically similar songbird species—hooded warbler (Setophaga citrina) and black‐throated blue warbler (Setophaga caerulescens)—that segregate over a climate gradient in the southern Appalachian Mountains, USA. Results: A simulation study indicated that the model can identify the effects of environmental variation and biotic interactions on co‐occurring species distributions. In the case study, there were strong and opposing effects of climate on spatial variation in population densities, but spatial competition did not influence the two species' distributions. Main Conclusions: Unlike existing species distribution models, the framework proposed here overcomes the MAUP and can be used to investigate how population‐level patterns emerge from individual‐level processes, while also allowing for inference on the spatial scale of biotic interactions. Our finding of minimal spatial competition between black‐throated blue warbler and hooded warbler adds to the growing body of literature suggesting that abiotic factors may be more important than competition at low‐latitude range margins. The model can be extended to accommodate count data and binary data in addition to SCR data. [ABSTRACT FROM AUTHOR] more...

A new type of Hawkes process, known as the fractional Hawkes Process (FHP), has been recently introduced. This process uses a Mittag-Leffler density as the kernel function which is asymptotically a power law and so similar to the Omori–Utsu law, suggesting the FHP may be an appropriate earthquake model. However, it is currently an unmarked point process meaning it is independent of an earthquake's magnitude. We extend the existing FHP, by incorporating Utsu's aftershock productivity law and a time-scaling parameter from the fractional Zener Model to a marked version so that it may better model earthquake aftershock sequences. We call this model the 'Seismic Fractional Hawkes Process' (SFHP). We then estimate parameters via maximum likelihood and provide evidence for these estimates being consistent and asymptotically normal via a simulation study. The SFHP is then compared to the epidemic type aftershock sequence and FHP models on four aftershock sequences from Southern California and New Zealand. While it is inconclusive if the seismic fractional Hawkes process performs better in a retrospective predictive performance experiment, it does perform favourably against both models in terms of information criteria and residual diagnostics especially when the aftershock clustering is stronger. [ABSTRACT FROM AUTHOR] more...

Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong. Therefore, we propose a fully nonparametric approach to testing significance of a covariate, taking into account the possible effects of nuisance covariates. Our tests match the nominal significance level, and their powers are comparable with the powers of parametric tests in cases where both the model for intensity function and the model for interactions are correct. When the parametric model for the intensity function is wrong, our tests achieve higher powers. The proposed methods rely on Monte Carlo testing and take advantage of the newly introduced concepts: the covariate-weighted residual measure and nonparametric residuals. We also define a correlation coefficient between a point process and a covariate and a partial correlation coefficient quantifying the dependence between a point process and a covariate of interest while removing the influence of nuisance covariates. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR] more...

Monitoring nociception, the flow of information associated with harmful stimuli through the nervous system even during unconsciousness, is critical for proper anesthesia care during surgery. Currently, this is done by tracking heart rate and blood pressure by eye. Monitoring objectively a patient's nociceptive state remains a challenge, causing drugs to often be over-or underdosed intraoperatively. Inefficient management of surgical nociception may lead to more complex postoperative pain management and side effects such as postoperative cognitive dysfunction, particularly in elderly patients. We collected a comprehensive and multisensor prospective observational dataset focused on surgical nociception (101 surgeries, 18,582 min, and 49,878 nociceptive stimuli), including annotations of all nociceptive stimuli occurring during surgery and medications administered. Using this dataset, we developed indices of autonomic nervous system activity based on physiologically and statistically rigorous point process representations of cardiac action potentials and sweat gland activity. Next, we constructed highly interpretable supervised and unsupervised models with appropriate inductive biases that quantify surgical nociception throughout surgery. Our models track nociceptive stimuli more accurately than existing nociception monitors. We also demonstrate that the characterizing signature of nociception learned by our models resembles the known physiology of the response to pain. Our work represents an important step toward objective multisensor physiology-based markers of surgical nociception. These markers are derived from an in-depth characterization of nociception as measured during surgery itself rather than using other experimental models as surrogates for surgical nociception. [ABSTRACT FROM AUTHOR] more...

AbstractThis article studies the properties of Hawkes process with a gamma memory kernel and a shape parameter α∈(0,1]. This process, called rough Hawkes process, is nearly unstable since its intensity diverges to +∞ for a very brief duration when a jump occurs. First, we find conditions that ensure the stability of the process and provide a closed form expression of the expected intensity. Second, we next reformulate the intensity as an infinite dimensional Markov process. Approximating these processes by discretization and then considering the limit leads to the Laplace transform of the point process. This transform depends on the solution of an elegant fractional integro-differential equation. The fractional operator is defined by the gamma kernel and is similar to the left-fractional Riemann-Liouville integral. We provide a simple method for computing the Laplace transform. This is easily invertible by discrete Fourier transform so that the probability density of the process can be recovered. We also propose two methods of simulation. We conclude the article by presenting the log-likelihood of the rough Hawkes process and use it to fit hourly Bitcoin log-returns from 9/2/18 to 9/2/23. [ABSTRACT FROM AUTHOR] more...

In this paper, we study the problem of predicting popularities of questions in Community Question Answering (CQA). To address this problem, we propose a Posterior Attention Recurrent Point Process Model (PARPP) to take both the interaction of users and the Matthew effect into account for question popularity prediction. Our PARPP uses long short-term memory (LSTM) to encode the observed history and another LSTM network to record each step of decoding information. At each decoding step, it uses prior attention to capture answers that have a greater impact on the problem. When a new answer is observed, it uses Bayes' rule to modify prior attention and obtain posterior attention. Then, the posterior attention is used to update the decoding status. We further introduce a convergence strategy to capture the Matthew effect in CQA. We conduct experiments on a Zhihu dataset crawled from a famous Chinese CQA forum. The experimental results show that our model outperforms several state-of-the-art methods. We further analyze the attention mechanism in our model. Our analysis shows that the proposed attention mechanism can better capture the impact of each answer on the future popularity of the question, which makes our model more interpretable. Our study would shed light on other similar studies such as answer ranking in response to the question and finding experts who have expertise on the topics of the questions. [ABSTRACT FROM AUTHOR] more...

Many techniques have been proposed to model space-varying observation processes with a nonstationary spatial covariance structure and/or anisotropy, usually on a geostatistical framework. Nevertheless, there is an increasing interest in point process applications, and methodologies that take nonstationarity into account are welcomed. In this sense, this work proposes an extension of a class of spatial Cox process using spatial deformation. The proposed method enables the deformation behavior to be data-driven, through a multivariate latent Gaussian process. Inference leads to intractable posterior distributions that are approximated via MCMC. The convergence of algorithms based on the Metropolis–Hastings steps proved to be slow, and the computational efficiency of the Bayesian updating scheme was improved by adopting Hamiltonian Monte Carlo (HMC) methods. Our proposal was also compared against an alternative anisotropic formulation. Studies based on synthetic data provided empirical evidence of the benefit brought by the adoption of nonstationarity through our anisotropic structure. A real data application was conducted on the spatial spread of the Spodoptera frugiperda pest in a corn-producing agricultural area in southern Brazil. Once again, the proposed method demonstrated its benefit over alternatives. [ABSTRACT FROM AUTHOR] more...

Evaluation metrics for prediction error, model selection and model averaging on space–time data are understudied and poorly understood. The absence of independent replication makes prediction ambiguous as a concept and renders evaluation procedures developed for independent data inappropriate for most space–time prediction problems. Motivated by air pollution data collected during California wildfires in 2008, this manuscript attempts a formalization of the true prediction error associated with spatial interpolation. We investigate a variety of cross-validation (CV) procedures employing both simulations and case studies to provide insight into the nature of the estimand targeted by alternative data partition strategies. Consistent with recent best practice, we find that location-based cross-validation is appropriate for estimating spatial interpolation error as in our analysis of the California wildfire data. Interestingly, commonly held notions of bias-variance trade-off of CV fold size do not trivially apply to dependent data, and we recommend leave-one-location-out (LOLO) CV as the preferred prediction error metric for spatial interpolation. [ABSTRACT FROM AUTHOR] more...

Marked temporal point process models (MTPPs) aim to model event sequences and event markers (associated features) in continuous time. These models have been applied to various application domains where capturing event dynamics in continuous time is beneficial, such as education systems, social networks, and recommender systems. However, current MTPPs suffer from two major limitations, i.e., inefficient representation of event dynamic's influence on marker distribution and losing fine-grained representation of historical marker distributions in the modeling. Motivated by these limitations, we propose a novel model called Marked Point Processes with Memory-Enhanced Neural Networks (MoMENt) that can capture the bidirectional interrelations between markers and event dynamics while providing fine-grained marker representations. Specifically, MoMENt is constructed of two concurrent networks: Recurrent Activity Updater (RAU) to capture model event dynamics and Memory-Enhanced Marker Updater (MEMU) to represent markers. Both RAU and MEMU components are designed to update each other at every step to model the bidirectional influence of markers and event dynamics. To obtain a fine-grained representation of maker distributions, MEMU is devised with external memories that model detailed marker-level features with latent component vectors. Our extensive experiments on six real-world user interaction datasets demonstrate that MoMENt can accurately represent users' activity dynamics, boosting time, type, and marker predictions, as well as recommendation performance up to 76.5%, 65.6%, 77.2%, and 57.7%, respectively, compared to baseline approaches. Furthermore, our case studies show the effectiveness of MoMENt in providing meaningful and fine-grained interpretations of user-system relations over time, e.g., how user choices influence their future preferences in the recommendation domain. [ABSTRACT FROM AUTHOR] more...

This study investigates the role of electrode density in capturing resting-state brain activity, an area of significant clinical relevance, where electroencephalography (EEG) is favored for its cost-efficiency. We analyze how different electrode configurations affect the precision of cortical current density estimation in EEG recordings. Using exact low-resolution electromagnetic tomography, we estimated the cortical current density in regions of interest linked to resting state networks. Point process analysis was employed to identify regions of high activity over time, revealing dynamic brain salient activity patterns, or brain maps. We evaluated the impact of electrode density by comparing 64-channel and 20-channel configurations and found that both configurations yielded similar and consistent brain maps. To confirm the robustness of our approach, we assessed the Berger effect in eyes-closed (EC) versus eyes-open (EO) conditions, observing that the functional differences between EC and EO states remained stable regardless of electrode density, aligning with previous research . Conversely, randomization of data or the use of non-homogeneous electrode configurations disrupted the resulting patterns, highlighting the physiological relevance of our methodology. Overall, our results demonstrate that this approach reliably captures the spatiotemporal dynamics of brain activity, even with fewer electrodes, and holds promise for broader clinical applications. more...

The realizability problem is a well-known problem in the analysis of complex systems, which can be modeled as an infinite-dimensional moment problem. More precisely, as a truncated K-moment problem where K is the space of all possible configurations of the components of the considered system. The power of this reformulation has been already exploited by Kuna, Lebowitz, and Speer [Ann. Appl. Probab. 21 (2011), pp. 1253–1281], where necessary and sufficient conditions of Haviland type have been obtained for several instances of the realizability problem. In this article we exploit this same reformulation to apply to the realizability problem the recent advances obtained by Curto, Ghasemi, Infusino, and Kuhlmann [J. Operator Theory 90 (2023), pp. 223–261] for the truncated moment problem for linear functionals on general unital commutative algebras. This provides alternative proofs and sometimes extensions of several results of Kuna, Lebowitz, and Speer [Ann. Appl. Probab. 21 (2011), pp. 1253–1281], allowing to finally embed them in the above-mentioned unified framework for the infinite-dimensional truncated moment problem. [ABSTRACT FROM AUTHOR] more...

We introduce a new fully non-parametric two-step adaptive bandwidth selection method for kernel estimators of spatial point process intensity functions based on the Campbell–Mecke formula and Abramson's square root law. We present a simulation study to assess its performance relative to other adaptive and global bandwidth selectors, investigate the influence of the pilot estimator and apply the technique to two data sets: A pattern of trees and an earthquake catalogue. [ABSTRACT FROM AUTHOR] more...

The Renewal Epidemic-Type Aftershock Sequence (RETAS) model is a recently proposed point process model that can fit event sequences such as earthquakes better than preexisting models. Evaluating the log-likelihood function and directly maximizing it has been shown to be a viable approach to obtain the maximum likelihood estimator (MLE) of the RETAS model. However, the direct likelihood maximization suffers from numerical issues such as premature termination of parameter searching and sensitivity to the initial value. In this work, we propose to use the Expectation-Maximization (EM) algorithm as a numerically more stable alternative to obtain the MLE of the RETAS model. We propose two choices of the latent variables, leading to two variants of the EM algorithm. As well as deriving the conditional distribution of the latent variables given the observed data required in the E-step of each EM-cycle, we propose an approximation approach to speed up the E-step. The resulting approximate EM algorithms can obtain the MLE much faster without compromising on the accuracy of the solution. These newly developed EM algorithms are shown to perform well in simulation studies and are applied to an Italian earthquake catalog. for this article are available online. [ABSTRACT FROM AUTHOR] more...

This article proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version. more...

Neurons respond to external stimuli and form functional networks through pairwise interactions. A neural encoding model can describe a single neuron’s behavior, and brain-machine interfaces (BMIs) provide a platform to investigate how neurons adapt, functionally connect, and encode movement. Movement modulation and pairwise functional connectivity are modeled as high-dimensional tuning states, estimated from neural spike train observations. However, accurate estimation of this neural state vector can be challenging as pairwise neural interactions are highly dimensional, change in different temporal scales from movement, and could be non-stationary. We propose an Adam-based gradient descent method to online estimate high-dimensional pairwise neuronal functional connectivity and single neuronal tuning adaptation simultaneously. By minimizing negative log-likelihood based on point process observation, the proposed method adaptively adjusts the learning rate for each dimension of the neural state vectors by employing momentum and regularizer. We test the method on real recordings of two rats performing the brain control mode of a two-lever discrimination task. Our results show that our method outperforms existing methods, especially when the state is sparse. Our method is more stable and faster for an online scenario regardless of the parameter initializations. Our method provides a promising tool to track and build the time-variant functional neural connectivity, which dynamically forms the functional network and results in better brain control. more...

Goal: REM Sleep Behavior Disorder (RBD) is a REM parasomnia that is associated to high risk of developing α-synucleinopathies, as Parkinson's disease (PD) or dementia with Lewy bodies, over time. This study aims at investigating the presence of autonomic dysfunctions in RBD subjects, with and without PD, by assessing their sleep structure and autonomous nervous system activity along the different sleep stages. Methods: To this aim, an innovative framework combining a sleep transition model, by Markov chains, with an instantaneous assessment of autonomic state dynamics by statistical modeling of heart rate variability (HRV) dynamics through a point-process approach, was introduced. Results: In general, RBD groups showed lower HRV than controls across all sleep stages, as well as higher probabilities of transitioning towards lighter sleep stages. Subjects also affected by PD present an even lower HRV, but better sleep continuity. Conclusions: RBD patients suffer from sleep fragmentation and overall autonomic dysfunction, mainly due to lower autonomic activation across all sleep stages. Coexistence of PD seems to improve sleep quality, possibly due to a sleep-related relief of their symptoms. more...

Convolutional neural networks (CNN) have shown great results for object-detection tasks by learning texture and pattern-extraction filters. However, object-level interactions are harder to grasp without increasing the complexity of the architectures. On the other hand, Point Process models propose to solve the detection of the configuration of objects as a whole, allowing the factoring in of the image data and the objects' prior interactions. In this paper, we propose combining the information extracted by a CNN with priors on objects within a Markov Marked Point Process framework. We also propose a method to learn the parameters of this Energy-Based Model. We apply this model to the detection of small vehicles in optical satellite imagery, where the image information needs to be complemented with object interaction priors because of noise and small object sizes. [ABSTRACT FROM AUTHOR] more...

In this paper, we study the extreme value behavior of the space-time process given by X i (t) = ∑ j ≥ 1 Ψ ij (t) Z i − j (t) , t ∈ [ 0 , 1 ] , i ∈ Z. We assume that { Z i (t) } t ∈ [ 0 , 1 ] , i ∈ Z is a sequence of i.i.d random fields on [ 0 , 1 ] with values in the Skorokhod space D [ 0 , 1 ] of càdlàg functions (i.e., right-continuous functions with left limits) D [ 0 , 1 ] equipped with the J1 topology. The coefficients { Ψ ij (t) } t ∈ [ 0 , 1 ] , i ∈ Z are processes with continuous sample paths. Our first aim is to establish a limit theory for point processes based on X(t). Secondly, using point processes, we study the limiting distribution of the normalized maximum process { a n − 1 max 1 ≤ i ≤ n X i (t) } t ∈ [ 0 , 1 ] . The result obtained in the second step can be viewed as extension of Balan who postponed the study of the behavior of maxima. It can also be considered as a generalization of Davis and Mikosch from deterministic real coefficients to random coefficients (Ψ ij) i ≥ 1 . [ABSTRACT FROM AUTHOR] more...

Consider the following migration process based on a closed network of N queues with $K_N$ customers. Each station is a $\cdot$ /M/ $\infty$ queue with service (or migration) rate $\mu$. Upon departure, a customer is routed independently and uniformly at random to another station. In addition to migration, these customers are subject to a susceptible–infected–susceptible (SIS) dynamics. That is, customers are in one of two states: I for infected, or S for susceptible. Customers can swap their state either from I to S or from S to I only in stations. More precisely, at any station, each susceptible customer becomes infected with the instantaneous rate $\alpha Y$ if there are Y infected customers in the station, whereas each infected customer recovers and becomes susceptible with rate $\beta$. We let N tend to infinity and assume that $\lim_{N\to \infty} K_N/N= \eta $ , where $\eta$ is a positive constant representing the customer density. The main problem of interest concerns the set of parameters of such a system for which there exists a stationary regime where the epidemic survives in the limiting system. The latter limit will be referred to as the thermodynamic limit. We use coupling and stochastic monotonicity arguments to establish key properties of the associated Markov processes, which in turn allow us to give the structure of the phase transition diagram of this thermodynamic limit with respect to $\eta$. The analysis of the Kolmogorov equations of this SIS model reduces to that of a wave-type PDE for which we have found no explicit solution. This plain SIS model is one among several companion stochastic processes that exhibit both random migration and contagion. Two of them are discussed in the present paper as they provide variants to the plain SIS model as well as some bounds and approximations. These two variants are the departure-on-change-of-state (DOCS) model and the averaged-infection-rate (AIR) model, which both admit closed-form solutions. The AIR system is a classical mean-field model where the infection mechanism based on the actual population of infected customers is replaced by a mechanism based on some empirical average of the number of infected customers in all stations. The latter admits a product-form solution. DOCS features accelerated migration in that each change of SIS state implies an immediate departure. This model leads to another wave-type PDE that admits a closed-form solution. In this text, the main focus is on the closed stochastic networks and their limits. The open systems consisting of a single station with Poisson input are instrumental in the analysis of the thermodynamic limits and are also of independent interest. This class of SIS dynamics has incarnations in virtually all queueing networks of the literature. [ABSTRACT FROM AUTHOR] more...

Neurons respond to external stimuli and form functional networks through pairwise interactions. A neural encoding model can describe a single neuron’s behavior, and brain-machine interfaces (BMIs) provide a platform to investigate how neurons adapt, functionally connect, and encode movement. Movement modulation and pairwise functional connectivity are modeled as high-dimensional tuning states, estimated from neural spike train observations. However, accurate estimation of this neural state vector can be challenging as pairwise neural interactions are highly dimensional, change in different temporal scales from movement, and could be non-stationary. We propose an Adam-based gradient descent method to online estimate high-dimensional pairwise neuronal functional connectivity and single neuronal tuning adaptation simultaneously. By minimizing negative log-likelihood based on point process observation, the proposed method adaptively adjusts the learning rate for each dimension of the neural state vectors by employing momentum and regularizer. We test the method on real recordings of two rats performing the brain control mode of a two-lever discrimination task. Our results show that our method outperforms existing methods, especially when the state is sparse. Our method is more stable and faster for an online scenario regardless of the parameter initializations. Our method provides a promising tool to track and build the time-variant functional neural connectivity, which dynamically forms the functional network and results in better brain control. [ABSTRACT FROM AUTHOR] more...

We present practical solutions to applying Gaussian‐process (GP) methods to calculate spatial statistics for grid cells in large environments. GPs are a data efficient approach to inferring neural tuning as a function of time, space, and other variables. We discuss how to design appropriate kernels for grid cells, and show that a variational Bayesian approach to log‐Gaussian Poisson models can be calculated quickly. This class of models has closed‐form expressions for the evidence lower‐bound, and can be estimated rapidly for certain parameterizations of the posterior covariance. We provide an implementation that operates in a low‐rank spatial frequency subspace for further acceleration, and demonstrate these methods on experimental data. [ABSTRACT FROM AUTHOR] more...

We show that if drift coefficients of Arratia flows converge in L 1 (R) or L ∞ (R) then the 1-point densities associated with these flows converge to the density for the flow with the limit drift. The main result is proven by providing a representation of the probability of coalescence in the flow as a solution to a PDE and applying the perturbation theory. [ABSTRACT FROM AUTHOR] more...

This article reviews some of the statistical issues involved with modeling SARS-CoV02 (Covid-19) in Los Angeles County, California, using Hawkes point process models and SEIR models. The two types of models are compared, and their pros and cons are discussed. We also discuss particular statistical decisions, such as where to place the upper limits on y-axes, and whether to use a Bayesian or frequentist version of the model, how to estimate seroprevalence, and fitting the density of transmission times in the Hawkes model. [ABSTRACT FROM AUTHOR] more...

We are concerned with zeros of random power series with coefficients being a stationary, centered, complex Gaussian process. We show that the expected number of zeros in every smooth domain in the disk of convergence is less than that of the hyperbolic Gaussian analytic function with i.i.d. coefficients. When coefficients are finitely dependent, i.e., the spectral density is a trigonometric polynomial, we derive precise asymptotics of the expected number of zeros inside the disk of radius r centered at the origin as r tends to the radius of convergence, in the proof of which we clarify that the negative contribution to the number of zeros stems from the zeros of the spectral density. [ABSTRACT FROM AUTHOR] more...

In this work, we perform an evaluation of the coverage of the earthquake monitoring network of Taiwan. The capability of a general network is a function of an adequate number of optimally distributed nodes. For this case study, the evaluation is performed with a statistical approach which includes descriptive spatial statistics in combination with point pattern techniques. The spatial distribution of the nodes of the earthquake monitoring network is analyzed in comparison with the distribution of seismicity, completeness magnitude, active seismogenic sources, seismic hazard, and population distribution. All these data can be put in relationship with the objectives of an earthquake monitoring network; therefore, they can be used, in turn, to retrieve information about the consistency of the network itself. In particular, we investigate the "Real-time Seismic Monitoring Network" and the "Strong-Motion Earthquake Observation Network," each one characterized by its own objectives, and therefore respectively compared with external information related to their purposes such as seismicity, seismogenic sources, seismic hazard, and population distribution. This simple and reliable approach reveals the high quality of the networks established in Taiwan. In general, it is able to provide quantitative information on the coverage of any type of network, identifying possible critical areas and addressing their future development. [ABSTRACT FROM AUTHOR] more...

The multivariate Hawkes process is a past-dependent point process used to model the relationship of event occurrences between different phenomena. Although the Hawkes process was originally introduced to describe excitation effects, which means that one event increases the chances of another occurring, there has been a growing interest in modelling the opposite effect, known as inhibition. In this paper, we focus on how to infer the parameters of a multidimensional exponential Hawkes process with both excitation and inhibition effects. Our first result is to prove the identifiability of this model under a few sufficient assumptions. Then we propose a maximum likelihood approach to estimate the interaction functions, which is, to the best of our knowledge, the first exact inference procedure in the frequentist framework. Our method includes a variable selection step in order to recover the support of interactions and therefore to infer the connectivity graph. A benefit of our method is to provide an explicit computation of the log-likelihood, which enables in addition to perform a goodness-of-fit test for assessing the quality of estimations. We compare our method to standard approaches, which were developed in the linear framework and are not specifically designed for handling inhibiting effects. We show that the proposed estimator performs better on synthetic data than alternative approaches. We also illustrate the application of our procedure to a neuronal activity dataset, which highlights the presence of both exciting and inhibiting effects between neurons. [ABSTRACT FROM AUTHOR] more...

An aggregated model is proposed, of which the partial-sum process scales to the Karlin stable processes recently investigated in the literature. The limit extremes of the proposed model, when having regularly-varying tails, are characterized by the convergence of the corresponding point processes. The proposed model is an extension of an aggregated model proposed by Enriquez (2004) in order to approximate fractional Brownian motions with Hurst index H 2 (0; 1=2), and is of a different nature of the other recently investigated Karlin models which are essentially based on infinite urn schemes. [ABSTRACT FROM AUTHOR] more...