Related papers: Continuous testing for Poisson process intensities…
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.…
Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and…
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…
We consider the problem of hypothesis testing in the situation where the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of different tests when…
We propose to test the homogeneity of a Poisson process observed on a finite interval. In this framework, we first provide lower bounds for the uniform separation rates in $\mathbb{L}^2$ norm over classical Besov bodies and weak Besov…
Statistical modeling of point patterns is an important and common problem in several areas. The Poisson process is the most common process used for this purpose, in particular, its generalization that considers the intensity function to be…
Considering two independent Poisson processes, we address the question of testing equality of their respective intensities. We first propose single tests whose test statistics are U-statistics based on general kernel functions. The…
Suppose we observe a Poisson process in real time for which the intensity may take on two possible values $\lambda_0$ and $\lambda_1$. Suppose further that the priori probability of the true intensity is not given. We solve a minimax…
We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a…
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,…
Many experiments are concerned with the comparison of counts between treatment groups. Examples include the number of successful signups in conversion rate experiments, or the number of errors produced by software versions in canary…
In this paper, we revisit the original ideas of Stein and propose an estimator of the intensity parameter of a homogeneous Poisson point process defined in $\R^d$ and observed in a bounded window. The procedure is based on a new general…
A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…
We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. We exhibit a prior on intensities which both leads to a computationally feasible method and enjoys…
Motivated by monitoring the arrival of incoming adverse events such as customer support calls or crash reports from users exposed to an experimental product change, we consider sequential hypothesis testing of continuous-time inhomogeneous…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…
This paper proposes a model of interactions between two point processes, ruled by a reproduction function h, which is considered as the intensity of a Poisson process. In particular, we focus on the context of neurosciences to detect…
Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…
This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…
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…