Related papers: Minimax Sequential Testing for Poisson Processes
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…
Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning. We formalize this learning task as the problem of sequentially testing how the minimum…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
An adapted, right-continuous, non-decreasing, integer-valued process with unit jumps and starting at zero has a minimal predictable intensity if and only if it is a standard Poisson process under an absolutely continuous transformation of…
We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…
Given a homogeneous Poisson process on ${\mathbb{R}}^d$ with intensity $\lambda$, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that…
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…
We consider the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution. This problem is investigated in a sequential setup under mild assumptions on the underlying random process. The…
We study a class of two-sided optimal control problems of general linear diffusions under a so-called Poisson constraint: the controlling is only allowed at the arrival times of an independent Poisson signal processes. We give a weak and…
In this work, based on a realization of an inhomogeneous Poisson process whose intensity function depends on a real unknown parameter, we consider a simple hypothesis against a sequence of close (contiguous) alternatives. Under certain…
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…
The purpose of this paper is to estimate the intensity of a Poisson process $N$ by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of $N$ with respect to $ndx$ where $n$ is a fixed…
While the Bayesian decision-theoretic framework offers an elegant solution to the problem of decision making under uncertainty, one question is how to appropriately select the prior distribution. One idea is to employ a worst-case prior.…
We study the problem of testing the goodness of fit of categorical count data to a Poisson distribution uniform over the categories, against a class of alternatives defined by excluding an $\ell_p$ ball, $p \leq 2$, of radius $\epsilon$…
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…
We study a Bayesian binary sequential hypothesis testing problem with multiple large language models (LLMs). Each LLM $j$ has per-query cost $c_j>0$, random waiting time with mean $\mu_j>0$ and sub-Gaussian tails, and \emph{asymmetric}…
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…
We construct a Bayesian sequential test of two simple hypotheses about the value of the unobservable drift coefficient of a Brownian motion, with a possibility to change the initial decision at subsequent moments of time for some penalty.…
The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…
We consider the problem of sensor selection for time-optimal detection of a hypothesis. We consider a group of sensors transmitting their observations to a fusion center. The fusion center considers the output of only one randomly chosen…