Markov Chain Monte Carlo

Marking a pivotal moment in the evolution of Bayesian inference, this third edition of this seminal textbook on Markov Chain Monte Carlo (MCMC) methods reflects the profound transformations in both the fields of statistics and the broader landscape of data science over the past two decades. Building on the foundations laid by its first two editions, this updated volume, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Third Edition, addresses the challenges posed by modern datasets, which now span millions or even billions of observations and high-dimensional parameter spaces. While faster, approximate methods have gained traction, MCMC remains the gold standard for rigorous and reliable Bayesian inference, and this book continues to champion its relevance in the face of evolving computational paradigms.

This latest edition introduces significant updates and expansions, including new material on infinite-dimensional MCMC, sequential Monte Carlo methods, and adaptive algorithms. It also revisits foundational topics with fresh insights, such as iterative dynamics, mixture distributions, and data augmentation, while incorporating cutting-edge developments like Hamiltonian Monte Carlo (HMC) and Dirichlet process-based methods. With a focus on both theoretical rigor and practical application, the book equips readers to navigate the complexities of modern Bayesian modeling and computation.

Features

• Expanded coverage of sequential Monte Carlo methods, complementing MCMC with probabilistic foundations
• A brand-new chapter on infinite-dimensional MCMC, addressing advanced stochastic simulation techniques for modern Bayesian modeling
• Enhanced theoretical treatment of Markov chains on continuous state spaces, including nonhomogeneous Markov chains and adaptive algorithms
• New sections on mixture distributions and data augmentation, showcasing their power in simplifying and improving MCMC algorithms
• Detailed exploration of HMC and Dirichlet process-based methods, reflecting recent advances in high-dimensional and scalable MCMC techniques
• Completely revised software section, aligning with contemporary Bayesian computation practices and tools, with accompanying R and Python codes available on GitHub

This textbook is an essential resource for statisticians, data scientists, and researchers in fields such as machine learning, artificial intelligence, and computational biology, who rely on Bayesian inference for analyzing complex, high-dimensional datasets. It is equally valuable for graduate students and academics seeking a comprehensive introduction to MCMC methods, as well as practitioners looking to deepen their understanding of modern Bayesian computation. With its blend of theoretical depth and practical guidance, this third edition serves as both a foundational text and a reference for advanced applications in the ever-expanding domain of Bayesian analysis.

Dani Gamerman:
Ph. D. in Statistics from University of Warwick in 1987. Professor of Statistics at UFRJ from 1996 to 2019. Professor Emeritus at UFRJ since 2021. Supervises graduate students and post-doctoral researchers.

Author of the books Statistical Inference: an Integrated Approach and Building a Platform for Data-Driven Pandemic Prediction: From Data Modelling to Visualisation - The CovidLP Project, both published by Chapman & Hall. Also published books and monographs in Portuguese.

Papers published in many statistical journals including Journal of the Royal Statistical Society, Series B & C, Biometrika, Bayesian Analysis, Annals of Applied Statistics, Statistics & Computing, and also in the multidisciplinary journal Science.

Foundational and Opening Lecturer at the 2024 and 2004 editions of the World Meeting of International Society for Bayesian Analysis (ISBA) and invited lecturer at BISP, International Meeting of the Psychometric Society, International Valencia Meeting on Bayesian Statistics and International Workshop on Statistical Modeling and at various other scientific meetings.

Visiting lecturer at UFMG, Carlos III-Madrid, Connecticut, University College London and Duke. Colaborador honorífico of Universidade Rey Juan Carlos in Madrid.

Invited seminars at many universities in Brazil and abroad.

Current Associate Editor of Statistical Modeling, International Statistical Review and Environmetrics. Former member of the Boards of Directors of ISBA and ABE (Brazilian Statistical Association). Elected member of ISI.

Organizer of many scientific meetings in Brazil.

Current research interests include: dynamic models, extreme value theory, item response thoery, spatial statistics, survival analysis, and Bayesian computation.

Hedibert Freitas Lopes:Full Professor, Insper Institute of Education and Research

He is a highly accomplished scholar in statistics and econometrics, currently serving as a Full Professor at the Insper Institute of Education and Research since 2013, where he leads the Data and Decision Sciences Unit. Previously, he held a decade-long tenure at the University of Chicago Booth School of Business. From 2021 to 2023, he served as the Charles Wexler Professor in Statistics in the School of Mathematical and Statistical Sciences at Arizona State University. Earlier in his teaching career, he held positions at the Fluminense Federal University and the Federal University of Rio de Janeiro.

Holding a PhD from the Institute of Statistics and Decision Sciences at Duke University, Professor Lopes has established a prolific academic record with about one hundred publications in selective journals. His research impact is substantial, evidenced by more than ten thousand citations on Google Scholar. Additionally, he has demonstrated a strong commitment to mentorship, having successfully supervised more than 40 graduate students, with several more currently ongoing.

Beyond his publications, Lopes is a recognized leader in the global statistical community, highlighted by his election as an ISI Fellow in 2020 and becoming the first Brazilian to be named an ISBA Fellow in 2024. His influence is further quantified by his extensive dissemination of knowledge, having delivered over two hundred invited talks and more than thirty short courses in universities, central banks, and other institutions around the world.

He actively leads major research initiatives, currently managing multiple projects focused on time series and high-dimensional data, and serves the academic community as a peer reviewer for over 100 international journals. He is currently an Associate Editor (AE) at the Journal of Computational and Graphical Statistics and has served for several years as AE for Bayesian Analysis, Journal of Business and Economic Statistics, and the Brazilian Journal of Probability and Statistics.

Flávio Bambirra Gonçalves:Holds a PhD in Statistics from the University of Warwick (2011). He is currently an Associate Professor of Statistics at the Federal University of Minas Gerais (UFMG), Brazil. His research interests lie broadly in Probability and Statistics, with particular emphasis on Bayesian statistics, stochastic processes, stochastic simulation, and computational statistics. His work also spans geostatistics, item response theory, and mathematical statistics.

He has been invited as a speaker to several scientific events and has undertaken multiple research visits as a visiting scholar at the Department of Statistics, University of Warwick. He maintains active research collaborations with national and international researchers and has published in leading statistics journals, including Journal of the Royal Statistical Society (Series B and C), Biometrika, Journal of the American Statistical Association, Journal of Computational and Graphical Statistics, and Statistics and Computing.

He has supervised and co-supervised several PhD and MSc students, contributing to the training of researchers in Bayesian computation, Monte Carlo methods, and statistical theory. He has been the recipient of highly competitive research grants in Brazil and served as President of the Brazilian Chapter of the International Society for Bayesian Analysis (ISBrA). His current research focuses on modern Monte Carlo methods, with particular interest in infinite-dimensional MCMC, Gaussian process models, and scalable Bayesian computation.