{"id":987,"date":"2025-08-28T11:13:27","date_gmt":"2025-08-28T11:13:27","guid":{"rendered":"https:\/\/sites.rutgers.edu\/nawaf-bou-rabee\/?page_id=987"},"modified":"2026-07-25T09:42:34","modified_gmt":"2026-07-25T09:42:34","slug":"book","status":"publish","type":"page","link":"https:\/\/sites.rutgers.edu\/nawaf-bou-rabee\/book\/","title":{"rendered":"Books"},"content":{"rendered":"<div class=\"reading-column\" style=\"max-width:760px;margin-left:auto;margin-right:auto\">\n<h2>Markov Chain Monte Carlo Methods<\/h2>\n<p><em>Nawaf Bou-Rabee and Andreas Eberle<\/em><\/p>\n<div style=\"text-align:center;margin:1em 0\"><img decoding=\"async\" style=\"max-width:540px;width:100%;height:auto;border-radius:4px\" src=\"https:\/\/sites.rutgers.edu\/nawaf-bou-rabee\/wp-content\/uploads\/sites\/908\/2026\/07\/mcmc_book_siebengebirge_3000x2400.png\" alt=\"A No-U-Turn Sampler on a seven-well potential drawn as a sepia topographic plate: level sets with wash shading, the chain\u2019s draws dusting the wells, and three transitions in red ink, each with leapfrog dots, a current state (open circle), and an accepted draw (gold dot).\" \/><\/div>\n<p style=\"color:#666;font-size:0.9em;max-width:540px;margin:0.4em auto 0;text-align:center;margin-bottom:2.5em\"><em>A No-U-Turn Sampler on a seven-well potential: the points are the chain\u2019s draws, and the red paths are three NUTS transitions, each from its current state (open circle) to the next draw (gold dot).<\/em><\/p>\n<p>Markov Chain Monte Carlo methods produce samples from a probability distribution that is known only up to a normalizing constant, by simulating a Markov process whose invariant distribution is the target. They are a basic tool of computational statistics and machine learning. This book gives a self-contained introduction to their design and to their quantitative analysis. The first part presents the main classes of methods: Metropolis&ndash;Hastings algorithms, Gibbs samplers, overdamped Langevin dynamics and its discretizations, auxiliary variable methods, Hamiltonian Monte Carlo and the No-U-turn sampler, and piecewise deterministic Markov processes. The second part develops the mathematical foundations of convergence to equilibrium: mixing and relaxation times, functional inequalities, couplings and transportation metrics, and quantitative bounds for ergodic averages. A third part treats advanced topics, including non-reversible lifts, MCMC methods on function spaces, MCMC methods for sequences of probability measures and their connections to diffusion modelling, and links to Riemannian geometry. The text grew out of graduate courses taught at Bonn and at Rutgers, and is intended for graduate students and researchers in mathematics, statistics, and machine learning.<\/p>\n<p>The book will be published by Birkh&auml;user in the series <a href=\"https:\/\/link.springer.com\/series\/11225\">Compact Textbooks in Mathematics<\/a>. Materials and updates related to the project will be posted on this page.<\/p>\n<p><!-- Figure provenance: terrain from SRTM elevation (AWS Terrain Tiles), lon 7.13-7.31, lat 50.636-50.706; target pi proportional to exp(0.028 x elevation in m); sampler: No-U-Turn Sampler (Hoffman-Gelman 2014, slice variant), leapfrog step 0.04 km, max tree depth 9; seven chains of 1500 iterations, one initialized at each of the seven summits (seeds 201-207); background shows all pooled draws and every computed leapfrog segment; featured transitions: seed 205 iteration 1113 (47 leapfrog steps), seed 202 iteration 236 (47), seed 207 iteration 707 (63), each terminated by the U-turn criterion; leapfrog energy drift below 1 percent along each featured orbit. --><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Markov Chain Monte Carlo Methods Nawaf Bou-Rabee and Andreas Eberle A No-U-Turn Sampler on a seven-well potential: the points are the chain\u2019s draws, and the red paths are three NUTS &hellip; <a href=\"https:\/\/sites.rutgers.edu\/nawaf-bou-rabee\/book\/\" class=\"\">Read More<\/a><\/p>\n","protected":false},"author":2614,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-custom.php","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-987","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Markov Chain Monte Carlo Methods \u2014 Book by Nawaf Bou-Rabee &amp; Andreas Eberle<\/title>\n<meta name=\"description\" content=\"Markov Chain Monte Carlo Methods, a graduate textbook by Nawaf Bou-Rabee and Andreas Eberle, to appear in the Birkhauser series Compact Textbooks in Mathematics.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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