陳冠宇(English version)
應用數學系副教授

聯絡方式

Email: gychen at math dot nctu dot edu dot tw
電話: 03-5712121 ext. 56421
傳真: 03-5724679
地址: 新竹市大學路1001國立交通大學 應用數學系
個人網頁: http://jupiter.math.nctu.edu.tw/~gychen/index.htm

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本學年度教授課程
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研究趣向

馬可夫鏈蒙地卡羅方法(簡稱為MCMC)是一個被廣泛運用的隨機演算法,其目的是要針對某一特定集合上的機率分布進行取樣模擬。一般而言,被取樣的機率分布其常態化係數是無法直接計算。因此,機率統計學家透過Metropolis-Hasting方法模擬一個馬可夫鏈,並設定其極限分布為被取樣分布。如此一來 便可透過馬可夫鏈的收斂性來逼近該機率分布。然而在時間是有限的前提下,MCMC的定性結果並不適用於實際模擬。針對這個問題,我們可以設定一個量測收斂性的標準,讓使用者可以根據該標準訂出不同的收斂需求,該需求反映在MCMC上即為一個演算法的停止時間。停止時間可以是確定的,也可以是隨機的,但時至今日沒有一個方法可以有效且準確地推算出演算法的停止時間。

馬可夫鏈的cutoff現象是該隨機 過程在演化時的相變現象。這個觀念是由AldousDiaconis在八零年代初期所提出,目的是要刻劃馬可夫鏈的機率分布在演化過程中的劇烈變化。簡而言之,在某個時間(相變時間)以前,馬可夫鏈的機率分布與極限分布的距離會處於最大值的狀態。接著在一段極短(相較於相變時間)的時間(相變區間)內,該距離函數會快速遞減,然後以指數速率收斂至零。當MCMC具有相變現象時,相變時間和相變區間提供了有效的演算停止時間。

MCMC演算法在其他領域的研究中也扮演了相當重要的角色,其中包含了統計物理學、資訊科學、分子生物學 和金融數學等等。從跨領域研究來看,MCMC演算法的模型可以非常複雜,例如不完整隨機媒體上的隨機漫步,或是緊緻黎曼流形上的馬氏過程。針對這類的問題,演算停止時間的計算將是很有挑戰性且受到高度期待的應用問題。

 

著作集
  1. Guan-Yu Chen and Yuan-Chung Sheu, On the log-Sobolev constant for the simple random walk on the n-cycle: the even cases. J. Funct. Anal. 202 (2003), 473-485.
  2. Guan-Yu Chen, Ken Palmer and Yuan-Chung Sheu, The least cost super replicating portfolio for short puts and calls in the Boyle-Vorst model with transaction costs. Advances in Quantitative Analysis of Finance and Accounting Vol. 5 (2007), 1-22.
  3. Guan-Yu Chen, Ken Palmer and Yuan-Chung Sheu The least cost super replication portfolio in the Boyle-Vorst model with transaction costs. International Journal of Theoretical and Applied Finance Vol. 11, No. 1 (2008), 55-85.
  4. Guan-Yu Chen and Laurent Saloff-Coste The cutoff phenomenon for randomized riffle shuffle. Random Structures and Algorithms 32 (2008), no. 3, 346-374.
  5. Guan-Yu Chen, Wai-Wai Liu and Laurent Saloff-Coste The logarithmic Sobolev constant of some finite Markov chains. Annales de la Faculte des Sciences de Toulouse Vol. XVII, No. 2 (2008), 239-290.
  6. Guan-Yu Chen and Laurent Saloff-Coste, The cutoff phenomenon for ergodic Markov processes. Electronic Journal of Probability, 13 (2008), 26-78.
  7. Guan-Yu Chen and Laurent Saloff-Coste, The L2-cutoff for reversible Markov processes. J. Funct. Anal. 258 (2010), 2246-2315.
  8. Guan-Yu Chen, Yang-Jen Fang and Yuan-Chung Sheu, The cutoff phenomenon for Ehrenfest chains. Stochastic Processes and their Applications, 122 (2012), 2830-2853.
  9. Guan-Yu Chen and Laurent Saloff-Coste, On the mixing time and spectral gap for birth and death chains. ALEA, Lat. Am. J. Probab. Math. Stat. Volume 10, Number 1 (2013), 293-321. arXiv:1304.4346
  10. Guan-Yu Chen and Laurent Saloff-Coste, Comparison of cutoffs between lazy walks and Markovian semigroups. J. Appl. Probab. Volume 50, Number 4 (2013), 943-959. arXiv:1304.4587
  11. Guan-Yu Chen and Laurent Saloff-Coste, Spectral computation for birth and death chains. Stochastic Processes and their Applications, 124 (2014), 848-882. arXiv:1305.0353
  12. Guan-Yu Chen and Laurent Saloff-Coste, Computing cutoff times for birth and death chains. Electronic Journal of Probability, 20 (2015), no. 76, 1-47. arXiv:1502.00361
  13. Guan-Yu Chen, Jui-Ming Hsu and Yuan-Chung Sheu, The L2-cutoff for reversible Markov chains, Annals of Applied Probability, 27 (2017), no. 4, 2305-2341. arXiv:1701.06663.
  14. Guan-Yu Chen and Takashi Kumagai, Cutoffs for product chains. (2017) To appear on Stochastic Processes and their Applications. arXiv:1701.06665.
  15. Guan-Yu Chen and Takashi Kumagai, Products of random walks on finite groups with moderate growth. (2017) To appear on Tohoku Mathematical Journal. arXiv:1703.05466.

最後更新日期:107/1/21