# Detecting Changes in Hidden Markov Models

## TL;DR

This paper develops optimal Shewhart tests for detecting changes in hidden Markov models under worst-case scenarios, balancing quick detection with false alarm constraints.

## Contribution

It introduces alternative formulations for change detection in hidden Markov models and derives optimal Shewhart tests for each, considering worst-case analysis.

## Key findings

- Optimal Shewhart tests maximize worst-case detection probability.
- The methods guarantee infrequent false alarms.
- New formulations improve robustness in change detection.

## Abstract

We consider the problem of sequential detection of a change in the statistical behavior of a hidden Markov model. By adopting a worst-case analysis with respect to the time of change and by taking into account the data that can be accessed by the change-imposing mechanism we offer alternative formulations of the problem. For each formulation we derive the optimum Shewhart test that maximizes the worst-case detection probability while guaranteeing infrequent false alarms.