Bayesian sequential monitoring of density estimates. (22nd December 2021) - Shamp, Wright; Linero, Antonio; Chicken, Eric
Abstract: In this paper, we consider sequentially estimating the density of univariate data. We utilize Pólya trees to develop a statistical process control (SPC) methodology. Our proposed methodology monitors the distribution of the sequentially observed data and detects when the generating density differs from an in‐control standard. We also propose an approximation that merges the probability mass of multiple possible changepoints to curb computational complexity while maintaining the accuracy of the monitoring procedure. We show in simulation experiments that our approach is capable of quickly detecting when a changepoint has occurred while controlling the number of false alarms, and performs well relative to competing methods. We then use our methodology to detect changepoints in high‐frequency foreign exchange (Forex) return data.