MCMC from Scratch: A Practical Introduction to Markov Chain Monte Carlo

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.

這本教科書介紹了馬可夫鏈蒙地卡羅（Markov Chain Monte Carlo，MCMC）的基礎知識，並不需要先備的高深數學和程式編寫知識。MCMC是一種強大的技術，可用於整合複雜函數或處理複雜的概率分佈。MCMC在統計方法重要的各個領域中經常被使用，例如貝葉斯統計、量子物理學、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，並使他們能夠自己編寫模擬代碼。

本書共分為六章。第二章介紹了蒙地卡羅算法，並強調了MCMC的優勢。第三章介紹了MCMC的一般性方面。第四章通過Metropolis算法的簡單示例說明了MCMC的本質。接著，第五章解釋了HMC算法、Gibbs抽樣算法和Metropolis-Hastings算法，討論了它們的優點、缺點和陷阱。最後，第六章介紹了MCMC的幾個應用。本書提供了豐富的例子和練習題及其解答，以及附錄中的示例代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是一個寶貴的資源。

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.

Masanori Hanada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將馬爾可夫鏈蒙特卡羅方法應用於超弦理論的先河。

So Matsuura是慶應義塾大學自然科學研究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摄動格點化。除了物理研究外，他對公眾宣傳活動有著強烈的熱情，並且舉辦了許多公開講座。