Information divergences and likelihood ratios of Poisson processes and point patterns

Autor:	Leskelä, Lasse
Rok vydání:	2024
Předmět:	Mathematics - Statistics Theory Computer Science - Information Theory Mathematics - Probability 62B10 60G55 94A17
Zdroj:	IEEE Transactions on Information Theory 2024 (early access)
Druh dokumentu:	Working Paper
DOI:	10.1109/TIT.2024.3472448
Popis:	This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical formulas for Kullback-Leibler divergences, R\'enyi divergences, Hellinger distances, and likelihood ratios of the laws of Poisson point patterns in terms of their intensity measures. The general results yield similar formulas for inhomogeneous Poisson processes, compound Poisson processes, as well as spatial and marked Poisson point patterns. Additional results include simple characterisations of absolute continuity, mutual singularity, and the existence of common dominating measures. The analytical toolbox is based on Tsallis divergences of sigma-finite measures on abstract measurable spaces. The treatment is purely information-theoretic and free of topological assumptions. Comment: Typos corrected
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.00294 Zobrazit plný text záznamu View this record from Arxiv