Statistical Process Control of the Stochastic Complexity of Discrete Processes

Changes in stochastic processes often affect their description length, and reflected by their stochastic complexity measures. Monitoring the stochastic complexity of a sequence (or, equivalently, its code length) can detect process changes that may be undetectable by traditional SPC methods. The context tree is proposed here as a universal compression algorithm for measuring the stochastic complexity of a state-dependent discrete process. The advantage of the proposed method is in the reduced number of samples that are needed for reliable monitoring.