請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69456完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳定立 | |
| dc.contributor.author | Chi-Hao Wu | en |
| dc.contributor.author | 吳其豪 | zh_TW |
| dc.date.accessioned | 2021-06-17T03:16:11Z | - |
| dc.date.available | 2023-07-19 | |
| dc.date.copyright | 2018-07-19 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-07-04 | |
| dc.identifier.citation | [1] Aldous, D.-J. and Fill, J.-A. Reversible Markov chains and random walks on graphs. 2002. URL: www.berkeley.edu/users/aldous/book.html.
[2] Chen, T.-L. and Hwang, C.-R. Accelerating reversible markov chains. Statistics and Probability Letters, 83(9):1956–1962, 2013. [3] Chen, T.-L., Chen, W.-K., C.-R. Hwang, C.-R., and Pai, H.-M. On the optimal transition matrix for markov chain monte carlo sampling. SIAM Journal on Control and Optimization, 50(5):2743–2762, 2012. [4] Diaconis, P. The markov chain monte carlo revolution. Bulletin of the American Mathematical Society, 46(2):179–205, 2009. [5] Frigessi, A., Hwang, C.-R., and Younes, L. Optimal spectral structure of reversible stochastic matrices, monte carlo methods and the simulation of markov random fields. The Annals of Applied Probability, 2(3):610–628, 1992. [6] Huang, L.-J., Liao, Y.-T., Chen, T.-L., and Hwang, C.-R. Optimal variance reduction for markov chain monte carlo. SIAM Journal on Control and Optimization. submitted. [7] Hwang, C.-R. Accelerating monte carlo markov processes. Cosmos, 1(9):87–94, 2005 [8] Iosifescu, M. Finite Markov processes and their applications. John Wiley, New York, 1980. [9] Peskun, P. H. Optimum monte carlo sampling using markov chains. Biometrika, 60(3):607–612, 1973. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69456 | - |
| dc.description.abstract | 馬可夫鏈蒙地卡羅法被廣泛運用於高維度分佈之抽樣，並且至今已經有大量的研究被投入於優化此演算法；無論是基於經驗法則或是理論證明，學界已經發現加速此演算法收斂速度的關鍵之一，是令演算法快速地漫步於抽樣空間裡。在這篇論文裡，我們算出演算法的漸進變異數與期望往返時間的關係；基於此我們證明了樹狀馬可夫鏈無法被均勻加速的猜法、提供了一個新的方法推導離散時間最優馬可夫鏈，並且更進一步推導出連續時間最優馬可夫過程。 | zh_TW |
| dc.description.abstract | Markov chain Monte Carlo(MCMC) is a popular strategy for sampling high dimensional distribution, and researches have been devoted to optimize the sampler. It has been known both heuristically and theoretically that a good sampler should travel fast among states in order to attain better convergence. In this thesis, the relation between the asymptotic variance of the sampler and the mean commute time is derived explicitly. Based on this relation, the conjecture in Chen and Hwang(2013) is shown rigorously; also, an alternative derivation of the optimal Markov chain presented in Chen et al.(2012) is given, and is further extended to construct the optimal Markov process under the average case criterion. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T03:16:11Z (GMT). No. of bitstreams: 1 ntu-107-R05246009-1.pdf: 383291 bytes, checksum: 7abcc396e3e4d0c15df6d2d8e02c93f4 (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | 目錄Contents
口試委員審定書i 誌謝ii 中文摘要iii Abstract iv 1 Introduction 1 2 The Optimal Transition Matrix of Markov Chain 5 2.1 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 The Asymptotic Variance of Reversible Markov Chain without Cycles 8 3.1 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4 The Optimal Transition Rate Matrix of Markov Process 15 4.1 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.1.1 Lower Bound of the Mean of the First Hitting Time . . . . . 15 4.1.2 Optimal Transition Rate Matrix . . . . . . . . . . . . . . . . 18 4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5 Conclusion 24 Reference 25 | |
| dc.language.iso | en | |
| dc.subject | 馬可夫鏈 | zh_TW |
| dc.subject | 馬可夫過程 | zh_TW |
| dc.subject | 收斂速率 | zh_TW |
| dc.subject | 漸進變異數 | zh_TW |
| dc.subject | 往返時間 | zh_TW |
| dc.subject | commute time | en |
| dc.subject | Markov process | en |
| dc.subject | Markov chain | en |
| dc.subject | convergence rate | en |
| dc.subject | asymptotic variance | en |
| dc.title | 基於期望往返時間之馬可夫鏈蒙地卡羅法收斂速率分析 | zh_TW |
| dc.title | On the Convergence Rate of Markov Chain Monte Carlo through Mean Commute Time | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 黃啟瑞,張志中,黃建豪 | |
| dc.subject.keyword | 馬可夫鏈,馬可夫過程,收斂速率,漸進變異數,往返時間, | zh_TW |
| dc.subject.keyword | Markov chain,Markov process,convergence rate,asymptotic variance,commute time, | en |
| dc.relation.page | 26 | |
| dc.identifier.doi | 10.6342/NTU201801291 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2018-07-05 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
| 顯示於系所單位： | 應用數學科學研究所 | |
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