MCMC from Scratch

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. 5explains 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.