Related papers: Marked spatial point processes: current state and …
The analysis of area-level aggregated summary data is common in many disciplines including epidemiology and the social sciences. Typically, Markov random field spatial models have been employed to acknowledge spatial dependence and allow…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
Aoristic data can be described by a marked point process in time in which the points cannot be observed directly but are known to lie in observable intervals, the marks. We consider Bayesian state estimation for the latent points when the…
We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases…
Point process modeling is gaining increasing attention, as point process type data are emerging in numerous scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression…
Advances in modern technology have enabled the simultaneous recording of neural spiking activity, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…
Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on…
In this paper, we analyze the asymptotic behavior of the point process of exceedances in a spatio-temporal setting whose points are given by the rescaled occurrence times, the sites and the rescaled values of exceedances. Here, the…
The marked Hawkes risk process is a compound point process for which the occurrence and amplitude of past events impact the future. Thanks to its autoregressive properties, it found applications in various fields such as neuosciences,…
Human activities generate various event sequences such as taxi trip records, bike-sharing pick-ups, crime occurrence, and infectious disease transmission. The point process is widely used in many applications to predict such events related…
Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump)…
We propose a latent self-exciting point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches that assume fully observable interactions, here we consider a…
Statistical network models are useful for understanding the underlying formation mechanism and characteristics of complex networks. However, statistical models for \textit{signed networks} have been largely unexplored. In signed networks,…
We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the…
We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
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…
Modern high-dimensional point process data, especially those from neuroscience experiments, often involve observations from multiple conditions and/or experiments. Networks of interactions corresponding to these conditions are expected to…