Handbook of Markov Chain Monte Carlo

Radu V. Craiu is a professor of statistics at the University of Toronto. His research interests are in computational methods in statistics, statistical inference, copula models, model selection procedures, and the use of statistical methods for scientific advancement in genetics, astronomy and demography. He is currently Contributing Editor for the IMS Bulletin and Associate Editor for the Harvard Data Science Review, Journal of Computational and Graphical Statistics, Statistics Surveys, The Canadian Journal of Statistics, and Statistical Methods and Applications. He received the CRM-SSC prize, is a Fellow of the Institute of Mathematical Statistics, a Fellow of the American Statistical Association, a Faculty Affiliate of the Vector Institute, and an Elected Member of the International Statistical Institute.Dootika Vats is an associate professor in the Department of Mathematics and Statistics at the Indian Institute of Technology Kanpur, India. Her research interests include output analysis for stochastic simulation, Markov chain Monte Carlo methods, proximal methods in Bayesian computation, and stochastic optimization. In 2021, she was one of the winners of the Blackwell-Rosenbluth Award given by the junior-International Society for Bayesian Analysis. She currently serves as an Associate Editor for Bayesian Analysis, Journal of Computational and Graphical Statistics, and Sankhya B.Galin L. Jones is Lynn Y. S. Lin Professor of Statistics and Director of the School of Statistics at the University of Minnesota. His primary research interests include Markov chain Monte Carlo, statistical theory and methods in both Bayesian and frequentist domains, as well as applications in neuroimaging and the physical sciences. He has collaborated with a wide range of researchers, including psychologists, veterinarians, librarians, ecologists, and astrophysicists, among others. Jones is an elected fellow of both the American Statistical Association and the Institute for Mathematical Statistics and is past Co-Editor of the Journal of Computational and Graphical Statistics.Steve Brooks is director and founder of Select Statistics, a statistical consultancy business based in the United Kingdom. He was formerly professor of Statistics at Cambridge University and received the Royal Statistical Society Guy medal in Bronze in 2005 and the Philip Leverhulme prize in 2004. Like his co-editors, he has served on numerous professional committees both in the United Kingdom and elsewhere, as well as sitting on numerous editorial boards. He is co-author of Bayesian Analysis for Population Ecology (Chapman & Hall/CRC, 2009) and co-founder of the National Centre for Statistical Ecology. His research interests include the development and application of computational statistical methodology across a broad range of application areas.Andrew Gelman is a professor of statistics and political science at Columbia University. His books include Bayesian Data Analysis (with John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin), Red State, Blue State, Rich State, Poor State: Why Americans Vote the Way They Do (with David Park, Boris Shor, and Jeronimo Cortina), Regression and Other Stories (with Jennifer Hill and Aki Vehtari), Active Statistics (with Aki Vehatri), and the forthcoming BayesianWorkflow (with many collaborators). He has done research on applications ranging from elections and public opinion to laboratory assays and toxicology; on the theory and practice of Bayesian statistical methods, from design and data collection through modeling, analysis, and model evaluation; and on statistical computing, graphics, and communication.Xiao-Li Meng is the Whipple V. N. Jones Professor of Statistics at Harvard, and the Founding Editor-in-Chief of Harvard Data Science Review. Meng received his BS in mathematics from Fudan University in 1982 and his PhD in statistics from Harvard in 1990. He was on the faculty of the University of Chicago from 1991 to 2001 before returning to Harvard, where he served as the Chair of the Department of Statistics (2004–2012) and the Dean of Graduate School of Arts and Sciences (2012–2017). His interests range from the theoretical foundations of statistical inferences (e.g., the interplay among Bayesian, Fiducial, and frequentist perspectives; frameworks for multi-source, multi-phase and multiresolution inferences) to statistical methods and computation (e.g., posterior predictive pvalue; EM algorithm; MCMC; bridge and path sampling) to applications in natural, social, and medical sciences and engineering (e.g., complex statistical modeling in astronomy and astrophysics, assessing disparity in mental health services, and quantifying statistical information in genetic studies). Meng was named the best statistician under the age of 40 by Committee of Presidents of Statistical Societies (COPSS) in 2001, and he was elected to the American Academy of Arts and Sciences in 2020.

• 1. Introduction to MCMC 2. MCMC using Hamiltonian Dynamics 3. Optimising and Adapting Metropolis Algorithm Proposal Distributions 4. How Many Iterations to Run? 5. Implementing MCMC: Multivariate Estimation with Confidence 6. Importance Sampling, Simulated Tempering, and Umbrella Sampling 7. Reversible Jump MCMC 8. Perfecting MCMC Sampling: Recipes and Reservations 9. The Data Augmentation Algorithm 10. Latent Gaussian Models and Computation for Large Spatial Data 11. Efficient MCMC in Astronomy 12. Computationally Intensive Inverse Problems 13. MCMC for State Space Models 14. MCMC Methods for Multi-modal Distributions 15. Algorithms for Models with Intractable Normalizing Functions 16. Involutive theory of MCMC 17. Unbiased MCMC 18. Control Variates for MCMC 19. Convergence Bounds for MCMC 20. Perturbations of Markov Chains 21. Running MCMC on Modern Hardware and Software 22. Bayesian Computation in Deep Learning 23. MCMC-driven Learning