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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳定立(Ting-Li Chen) | |
| dc.contributor.author | Chen-Wei Hua | en |
| dc.contributor.author | 華振崴 | zh_TW |
| dc.date.accessioned | 2021-06-17T07:08:10Z | - |
| dc.date.available | 2021-07-25 | |
| dc.date.copyright | 2019-07-25 | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2019-07-23 | |
| dc.identifier.citation | Aldous, D.-J., & Fill, J.-A. (2002). Reversible markov chains and random walks on graphs. URL www.berkeley.edu/users/aldous/book.html.
Chen, T.-L., Chen, W.-K., Hwang, C.-R., & Pai, H.-M. (2012). On the optimal transition matrix for markov chain monte carlo sampling. SIAM Journal on Control and Optimization, 50(5), 2743–2762. Chen, T.-L., & Hwang, C.-R. (2013). Accelerating reversible markov chains. Statistics and Probability Letters, 83(9), 1956–1962. Diaconis, P., Holmes, S., & Neal, R. (2000). Analysis of non-reversible markov chain sampler. The Annals of Applied Probability, 10(3), 726–752. Frigessi, A., Hwang, C.-R., & Younes, L. (1992). 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. Geman, S., & Geman, D. (1984). Stochastic relaxation, gibbs distributions and the bayesian restoration of images. IEEE Transactions on pattern analysis and machine intelligence, 6(6), 721–741. Hastings, W. K. (1970). Monte carlo sampling methods using markov chains and their applications. Biometrika, 57(1), 97–109. Huang, L.-J., Liao, Y.-T., Chen, T.-L., & Hwang, C.-R. (2018). Optimal variance reduction for markov chain monte carlo. SIAM Journal on Control and Optimization, 56(4), 2977–2996. Hwang, C.-R., Hwang-Ma, S.-Y., & Sheu, S.-J. (1993). Accelerating gaussian diffusions. The Annals of Applied probability, 3(3), 897–913. Hwang, C.-R., Hwang-Ma, S.-Y., & Sheu, S.-J. (2005). Accelerating diffusions. The Annals of Applied probability, 15(2), 1433–1444. Iosifescu, M. (1980). Finite markov processes and their applications. New York: John Wiley. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21(6), 1087–1092. Mira, A., & Geyer, C.-J. (2000). On non-reversible markov chains. Fields Institution Communications, 26, 93–108. Peskun, P. H. (1973). Optimum monte carlo sampling using markov chains. Biometrika, 60(3), 607–612. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/72853 | - |
| dc.description.abstract | Chen and Hwang, 2013 proposed to improve a reversible Markov chain by adding an antisymmetric perturbation on a cycle. Since the perturbed Markov chain is no longer reversible, one can not iteratively apply this antisymmetric perturbation method on different cycles. Chen and Hwang, 2013 also showed that the method works on disjoint cycles. In this paper, we further investigate the case of two cycles sharing the same vertex. We will show that the method can work on two cycles under some additional conditions. In addition to the theory, we implement the antisymmetric perturbation method on the Ising model. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T07:08:10Z (GMT). No. of bitstreams: 1 ntu-108-R06221004-1.pdf: 1968629 bytes, checksum: 749d3cba8f69dadd5349b09cd07970b4 (MD5) Previous issue date: 2019 | en |
| dc.description.tableofcontents | Abstract i
誌謝 ii Contents iii 1 Introduction 1 2 Theoretical result 5 3 Multiple acceleration on the Ising model 9 4 Conclusion 21 Bibliography 22 A Proof of lemma 7 and further discussion 23 B Graphs for Gibbs sampler 28 | |
| dc.language.iso | en | |
| dc.subject | 漸近變異數 | zh_TW |
| dc.subject | 馬可夫鏈蒙地卡羅 | zh_TW |
| dc.subject | 馬可夫鏈 | zh_TW |
| dc.subject | 收斂速度 | zh_TW |
| dc.subject | 可逆馬可夫鏈 | zh_TW |
| dc.subject | antisymmetric perturbation | en |
| dc.subject | asymptotic variance | en |
| dc.subject | reversibility | en |
| dc.subject | rate of convergence | en |
| dc.subject | Markov chain Monte Carlo | en |
| dc.title | 可逆馬可夫鏈之多重加速 | zh_TW |
| dc.title | Multiple Acceleration on Reversible Markov Chain | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 107-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 黃啟瑞(Chii-Ruey Huang),張志中(Chih-Chung Chang),黃建豪(Chien-Hao Huang) | |
| dc.subject.keyword | 馬可夫鏈,馬可夫鏈蒙地卡羅,收斂速度,漸近變異數,可逆馬可夫鏈, | zh_TW |
| dc.subject.keyword | Markov chain Monte Carlo,rate of convergence,reversibility,asymptotic variance,antisymmetric perturbation, | en |
| dc.relation.page | 29 | |
| dc.identifier.doi | 10.6342/NTU201901764 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2019-07-24 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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