Toward Uncertainty Aware Quickest Change Detection

Abstract

We study the problem of Quickest Change Detection (QCD) where the parameters of both the pre- and post-change distributions are completely unknown or known within a second-order distribution generated from training data. We propose the use of the Uncertain Likelihood Ratio (ULR) test statistic, which is designed from a Bayesian perspective in contrast with the traditional frequentist approach, i.e., the Generalized Likelihood Ratio (GLR) test. The ULR test utilizes a ratio of posterior predictive distributions, which incorporates parameter uncertainty into the likelihood estimates when there is a lack of or limited availability of training samples. Through an empirical study, we show that the proposed test outperforms the GLR test, while achieving similar results as the classical CUSUM algorithm as the number of training samples goes to infinity.

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