A Binning Approach to Quickest Change Detection With Unknown Post-Change Distribution

The problem of quickest detection of a change in distribution is considered under the assumption that the prechange distribution is known, and the postchange distribution is only known to belong to a family of distributions distinguishable from a discretized version of the prechange distribution. A sequential change detection procedure is proposed that partitions the sample space into a finite number of bins and monitors the number of samples falling into each of these bins to detect the change. A test statistic that approximates the generalized likelihood ratio test is developed. It is shown that the proposed test statistic can be efficiently computed using a recursive update scheme, and a procedure for choosing the number of bins in the scheme is provided. Various asymptotic properties of the test statistic are derived to offer insights into its performance tradeoff between average detection delay and average run length to false alarm. Testing on synthetic and real data demonstrates that our approach is comparable or better in the performance to existing nonparametric change detection methods.