Bayesian Switching Multiple Disorder Problems
研究了可观测布朗运动在切换常数漂移率下的贝叶斯切换多重异常问题，通过将初始问题转化为三维扩散后验概率过程的最优切换问题，推导了贝叶斯风险函数和最优切换边界的解析估计。
The switching multiple disorder problem seeks to determine an ordered infinite sequence of times of alarms which are as close as possible to the unknown times of disorders, or change-points, at which the observable process changes its probability characteristics. We study a Bayesian formulation of this problem for an observable Brownian motion with switching constant drift rates. The method of proof is based on the reduction of the initial problem to an associated optimal switching problem for a three-dimensional diffusion posterior probability process and the analysis of the equivalent coupled parabolic-type free-boundary problem. We derive analytic-form estimates for the Bayesian risk function and the optimal switching boundaries for the components of the the posterior probability process.