Textbook in PDF format This thoroughly revised and expanded second edition of the Handbook of Markov Chain Monte Carlo reflects the dramatic evolution of MCMC methods since the publication of the first edition. With the addition of two new editors, Radu V. Craiu and Dootika Vats, this comprehensive reference now offers deeper insights into the theoretical foundations and cutting-edge developments that are reshaping the field. Key Features: Completely restructured content with 13 updated chapters from the first edition and ten entirely new chapters reflecting the latest methodological advances In-depth coverage of recent breakthroughs in multi-modal sampling, intractable likelihood problems, and involutive MCMC theory Comprehensive exploration of unbiased MCMC methods, control variates, and rigorous convergence bounds Practical guidance on implementing MCMC algorithms on modern hardware and software platforms Cutting-edge material on the integration of MCMC with deep learning and other machine learning approaches Authoritative treatment of theoretical foundations alongside practical implementation strategies This essential reference serves statisticians, computer scientists, physicists, data scientists, and researchers across disciplines who employ computational methods for Bayesian inference and stochastic simulation. Graduate students will find it an invaluable learning resource, while experienced practitioners will appreciate its balance of theoretical depth and practical implementation advice. Whether used as a comprehensive guide to current MCMC methodology or as a reference for specific advanced techniques, this handbook provides the definitive resource for anyone working at the intersection of Bayesian computation and modern statistical modeling