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Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial…
The intensity matching approach for tractable performance evaluation and optimization of cellular networks is introduced. It assumes that the base stations are modeled as points of a Poisson point process and leverages stochastic geometry…
Non-homogeneous Poisson processes are used in a wide range of scientific disciplines, ranging from the environmental sciences to the health sciences. Often, the central object of interest in a point process is the underlying intensity…
To model recurrent interaction events in continuous time, an extension of the stochastic block model is proposed where every individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous…
Recent years have seen an increased interest in the application of methods and techniques commonly associated with machine learning and artificial intelligence to spatial statistics. Here, in a celebration of the ten-year anniversary of the…
Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e. a nonlinear shift along the time axis,…
We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Our model combines the techniques…
We observe $n$ inhomogeneous Poisson processes with covariates and aim at estimating their intensities. We assume that the intensity of each Poisson process is of the form $s (\cdot, x)$ where $x$ is the covariate and where $s$ is an…
The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non-parametric regression and classification. A BART scheme for estimating the intensity of inhomogeneous Poisson…
Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…
Modelling the first-order intensity function is one of the main aims in point process theory, and it has been approached so far from different perspectives. One appealing model describes the intensity as a function of a spatial covariate.…
The availability of large spatial data geocoded at accurate locations has fueled a growing interest in spatial modeling and analysis of point processes. The proposed research is motivated by the intensity estimation problem for large…
We consider a doubly stochastic Poisson process with stochastic intensity $\lambda_t =n q\left(X_t\right)$ where $X$ is a continuous It\^o semimartingale and $n$ is an integer. Both processes are observed continuously over a fixed period…
The paper considers a Cox process where the stochastic intensity function for the Poisson data model is itself a non-homogeneous Poisson process. We show that it is possible to obtain the marginal data process, namely a non-homogeneous…
This paper discusses properties of a Doubly Stochastic Poisson Process (DSPP) where the intensity process belongs to a class of affine diffusions. For any intensity process from this class we derive an analytical expression for probability…
We consider a road network represented by a directed graph. We assume to collect many measurements of traffic flows on all the network arcs, or on a subset of them. We assume that the users are divided into different groups. Each group…
Learning the dynamics of spatiotemporal events is a fundamental problem. Neural point processes enhance the expressivity of point process models with deep neural networks. However, most existing methods only consider temporal dynamics…
We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through…
We develop a (nearly) unbiased particle filtering algorithm for a specific class of continuous-time state-space models, such that (a) the latent process $X_t$ is a linear Gaussian diffusion; and (b) the observations arise from a Poisson…
Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or…