臺灣博碩士論文加值系統

　　現在MCMC是一個普遍被使用的高維數值積分法。在這篇文章中，我們將會探討一種Wong and Liang 於1997年的動態加權的MCMC，這種方法會使我們的馬可夫鏈收斂得更加精準。在過去十幾年中，Metropolis-Hasting演算法一直扮演著MCMC中很重要的角色，但是這種方法仍存在著不少待克服的問題。例如說，整個馬可夫過程的移動很容易被一些小機率的狀態影響，這種現象會直接反應在我們的模擬結果上。我們主要回顧了加權MCMC的方法，並在一些特殊的設定下給出一個理論證明，透過這個方法，我們可以使原本的MCMC收斂的更有效率。

Markov Chain Monte Carlo method is a universal-used method in numerical integration. In this talk, we will discuss the dynamic weighting MCMC proposed by Wong and Liang (1997), which makes the Markov chain converges faster. In the decades, Metropolis Hasting algorithm is an important simulation method, but there are still some drawbacks in the simulation. For example, the movement of the process can be influenced by some tiny probability nodes. This phenomenon may directly affect to our simulated estimation. Our main work is to review the weighted MCMC and give some theoretical proof in some special cases. Through the manner, we can make the MCMC method more efficient.

Contents
Abstract(in Chinese) i
Abstract(in English) ii
Acknowledgements(in Chinese) iii
Contents v
1 Introduction 1
2 Two states analysis (I) 2
3 Two states analysis (II) 9
4 Simulation and Other Results 19
5 Conclusions and Discussion 28
Reference 30

Reference
1. Wong, W. H., & Liang, F. (1997). Dynamic weighting in Monte Carlo and optimization.
Proceedings of the National Academy of Sciences, 94(26), 14220-14224.
2. Liu, J. S., Liang, F., & Wong, W. H. (2001). A theory for dynamic weighting in Monte Carlo
computation. Journal of the American Statistical Association, 96(454), 561-573.
3. Norris, J. R. (1998). Markov chains (No. 2008). Cambridge university press.
4. Ross, S. M. (2002) . Simulation . Academic Press.
5. Cinlar, E. (2013). Introduction to stochastic processes. Courier Corporation.
30