動態系統的貝氏分析

Abstract

在過去數年，我們已經相當程度探索Woodroofe-Stein 等式\r\n及其在序貫分析和貝式統計之應用。本計畫著重在動態模型\r\n之應用及其與卡爾曼fileter 之關聯 。我們得到一種新的方\r\n法來推導卡爾曼增益(Kalman gain)。本計畫之副產品是將目\r\n前Woodroofe-Stein 等式進一步推展， 得到多元的Gram-\r\nCharlier 級數。\r\nIn the past years we have explored Woodroofe-Stein"s\r\nidentity and its applications to sequential analysis\r\nand Bayesian statistics. This project focused on its\r\napplication to dynamic models and relation to Kalman\r\nfileter. We provide a new approach to obtain the\r\nKalman gain. A by-product of this project is to take\r\nthe present Woodroofe-Stein"s identity one step\r\nfurther to obtain the multivariate Gram-Charlier\r\nseries.