MCMC from Scratch: A Practical Introduction to Markov Chain Monte Carlo
暫譯: 從零開始的MCMC：馬可夫鏈蒙地卡羅實務入門
Hanada, Masanori, Matsuura, So
商品描述
This textbook explains the fundamentals of Markov Chain Monte Carlo (MCMC) without assuming advanced knowledge of mathematics and programming. MCMC is a powerful technique that can be used to integrate complicated functions or to handle complicated probability distributions. MCMC is frequently used in diverse fields where statistical methods are important - e.g. Bayesian statistics, quantum physics, machine learning, computer science, computational biology, and mathematical economics. This book aims to equip readers with a sound understanding of MCMC and enable them to write simulation codes by themselves.
The content consists of six chapters. Following Chap. 2, which introduces readers to the Monte Carlo algorithm and highlights the advantages of MCMC, Chap. 3 presents the general aspects of MCMC. Chap. 4 illustrates the essence of MCMC through the simple example of the Metropolis algorithm. In turn, Chap. 5 explains the HMC algorithm, Gibbs sampling algorithm and Metropolis-Hastings algorithm, discussing their pros, cons and pitfalls. Lastly, Chap. 6 presents several applications of MCMC. Including a wealth of examples and exercises with solutions, as well as sample codes and further math topics in the Appendix, this book offers a valuable asset for students and beginners in various fields.
商品描述(中文翻譯)
這本教科書解釋了馬可夫鏈蒙地卡羅（Markov Chain Monte Carlo, MCMC）的基本原理，並不假設讀者具備高級數學和程式設計的知識。MCMC 是一種強大的技術，可用於整合複雜的函數或處理複雜的機率分佈。MCMC 在許多統計方法重要的領域中被廣泛使用，例如貝葉斯統計、量子物理、機器學習、計算機科學、計算生物學和數學經濟學。本書旨在使讀者對 MCMC 有深入的理解，並能夠自行撰寫模擬程式碼。
內容共分為六章。第二章介紹了蒙地卡羅演算法並強調了 MCMC 的優勢，第三章則介紹了 MCMC 的一般性質。第四章通過簡單的梅特羅波利斯（Metropolis）演算法範例來說明 MCMC 的本質。接著，第五章解釋了哈密頓蒙地卡羅（HMC）演算法、吉布斯取樣（Gibbs sampling）演算法和梅特羅波利斯-哈斯廷斯（Metropolis-Hastings）演算法，討論它們的優缺點及陷阱。最後，第六章介紹了 MCMC 的幾個應用。這本書包含大量的範例和練習題及其解答，還有附錄中的範例程式碼和進一步的數學主題，對於各個領域的學生和初學者來說，都是一個寶貴的資源。
作者簡介
Masanori Hanada is a theoretical physicist at the Department of Mathematics, the University of Surrey. His research interests include strongly coupled quantum systems, quantum field theory, and superstring theory. He and his collaborators pioneered the application of Markov Chain Monte Carlo methods for superstring theory.
So Matsuura is a theoretical physicist at Research and Education Center for Natural Sciences, Keio University. His research interests include superstring theory and nonperturbative lattice formulation of supersymmetry quantum field theory. In addition to physics research, he has a strong passion for public outreach activities and delivers many public lectures.
作者簡介(中文翻譯)
花田正則是薩里大學數學系的理論物理學家。他的研究興趣包括強耦合量子系統、量子場論和超弦理論。他和他的合作者開創了馬可夫鏈蒙地卡羅方法在超弦理論中的應用。
松浦宗是慶應義塾大學自然科學研究與教育中心的理論物理學家。他的研究興趣包括超弦理論和超對稱量子場論的非微擾格點形式。除了物理研究外，他對公共宣傳活動充滿熱情，並進行了許多公共講座。
