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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/77379


    Title: 動態系統的貝氏分析
    Other Titles: Bayesian Inference for Some Dynamic Systems
    Authors: 翁久幸
    Contributors: 統計學系
    Keywords: 貝氏分析;動態系統;卡爾曼渡波;Woodroofe-Stein等式
    Bayesian inference;dynamic systems;Kalman filter;Woodroofe-Stein`s identity
    Date: 2014
    Issue Date: 2015-08-05 12:08:57 (UTC+8)
    Abstract: Weng and Lin (JMLR 2011)應用Woodroofe-Stein等式提出一個貝氏近似方法，以此 來推導出一套線上比賽參與者能力的排名演算法，適用於序貫觀察之大型資料.該演 算法應用於Xbox beta測試之資料的預測能力與Microsoft之TrueSkill演算法相當， 但演算法本身精簡許多. 這一個演算法及貝氏近似方法很快地被套用到其他問題，例如Wistubaetal. (2012) 修改Weng and Lin的演算法以適用於預測電腦圍棋之棋步；Chen et al. (2013)將 我們的貝氏近似方法應用於crowdsourced之情境，並得出一個有效率的線上貝氏排 名系統. 這裡所謂的線上學習方法指的是新資料可能不斷地增加，統計模型跟著不斷地更新， 當資料被使用之後，基於儲存等考量，就不再保留，故對於資料量極為龐大之實際問 題，線上學習之方法有其必要.於當今資料爆炸的年代，這類方法更形重要. 鑑於以上關於Woodroofe-Stein等式在線上機器學習之諸多應用，本研究擬進一步探 討如何將此方法連接到若干需要使用線上方法之領域，比方一些動態線性系統，如卡 爾曼渡波；其次考慮非線性系統.除此之外，本研究計晝擬針對Woodroofe-Stein等 式作一回顧性論文：說明其與著名的Stein’s lemma之關聯，其如何被用來得出 AR(p)模型參數估計之誤差，其如何從一 frequentist統計之工具發展至貝氏統計 分析，而至貝氏線上方法.
    Weng and Lin (JMLR 2011) used a Bayesian approximate moment-matching scheme based on Woodroofe-Stein’s identity to derive an online ranking algorithm for updating players’ skills in the scenario where game data arrive sequentially. The performance of this algorithm on Xbox beta testing data is competitive with state of the art systems such as TrueSkill, but the running time and the code are much shorter. The online ranking algorithm and Bayesian moment-matching scheme proposed in Weng and Lin (2011) were adopted by other researchers in different applications. For example, Wistuba et al. (2012) modified this ranking algorithm for move prediction with the game of computer Go; Chen et al. (2013) applied this moment-matching scheme to obtain an efficient online Bayesian ranking scheme in a crowdsourced setting. The online method here refers to learning methods that process data sequentially, and the data can be removed after being processed. This method is useful for data that is large and arrives sequentially. In view of its usefulness for online learning, we are interested in studying how this Bayesian method can be applied to some other dynamic models, where large data arrives sequentially and online methods are desired; for exmaple, the Kalman filter. In addition, we plan to conduct a survey about Woodroofe-Stein’s identity: explaining its relation to the famous Stein’s lemma, explaining the theoretical developments from frequentist to Bayesian, and showing how it has been applied in different areas.
    Relation: NSC102-2118-M004-003-MY2
    PA10301-0237
    Data Type: report
    Appears in Collections:[統計學系] 國科會研究計畫

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