Markov Chain Monte Carlo
Metropolis–Hastings, Gibbs, HMC, and NUTS.
Markov Chain Monte Carlo. Metropolis–Hastings, Gibbs, HMC, and NUTS.
Foundations and canonical references
The standard treatments of markov chain monte carlo approach the subject from complementary angles. Brooks, Handbook of Markov Chain Monte Carlo (2011) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Robert, Monte Carlo Statistical Methods (2004) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for markov chain monte carlo include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2011Handbook of Markov Chain Monte Carlobrooks-2011, gelman-2011, jones-2011, meng-2011
- textbook · primary · 2004Monte Carlo Statistical Methodsrobert-2004, casella-2004
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