English

Minimax Sequential Testing for Poisson Processes

Statistics Theory 2025-04-25 v2 Optimization and Control Statistics Theory

Abstract

Suppose we observe a Poisson process in real time for which the intensity may take on two possible values λ0\lambda_0 and λ1\lambda_1. Suppose further that the priori probability of the true intensity is not given. We solve a minimax version of Bayesian problem of sequential testing of two simple hypotheses to minimize a linear combination of the probability of wrong detection and the expected waiting time in the worst scenario of all possible priori distributions. An equivalent characterization for the least favorable distributions is derived and a sufficient condition for the existence is concluded.

Keywords

Cite

@article{arxiv.2311.04084,
  title  = {Minimax Sequential Testing for Poisson Processes},
  author = {Hongwei Mei},
  journal= {arXiv preprint arXiv:2311.04084},
  year   = {2025}
}