Change Detection of Markov Kernels with Unknown Pre and Post Change Kernel

TL;DR

This paper introduces a new change detection algorithm for Markov kernels in metric spaces, capable of identifying changes even when the post-change kernel is unknown, with proven bounds on performance.

Contribution

The paper presents a novel change detection method for Markov kernels with unknown post-change kernels, under uniform ergodicity assumptions.

Findings

Derived upper bound on mean delay

Established lower bound on false alarm interval

Numerical simulations confirm effectiveness

Abstract

In this paper, we develop a new change detection algorithm for detecting a change in the Markov kernel over a metric space in which the post-change kernel is unknown. Under the assumption that the pre- and post-change Markov kernel is uniformly ergodic, we derive an upper bound on the mean delay and a lower bound on the mean time between false alarms. A numerical simulation is provided to demonstrate the effectiveness of our method.