Sequential Monitoring of a Bernoulli Sequence when the Pre-change Parameter is Unknown

TL;DR

This paper introduces a new, computationally efficient change detection method for Bernoulli sequences using Fisher's Exact Test, effective even when the pre-change parameter is unknown, and demonstrates its performance through simulations.

Contribution

A novel change detection approach based on Fisher's Exact Test that operates efficiently without prior knowledge of the pre-change Bernoulli parameter.

Findings

Method performs comparably to optimal CUSUM in simulations

Efficient implementation suitable for real-time monitoring

Effective when pre-change parameter is unknown

Abstract

The task of monitoring for a change in the mean of a sequence of Bernoulli random variables has been widely studied. However most existing approaches make at least one of the following assumptions, which may be violated in many real-world situations: 1) the pre-change value of the Bernoulli parameter is known in advance, 2) computational efficiency is not paramount, and 3) enough observations occur between change points to allow asymptotic approximations to be used. We develop a novel change detection method based on Fisher's Exact Test which does not make any of these assumptions. We show that our method can be implemented in a computationally efficient manner, and is hence suited to sequential monitoring where new observations are constantly being received over time. We assess our method's performance empirically via using simulated data, and find that it is comparable to the optimal CUSUM scheme which assumes both pre- and post-change values of the parameter to be known.