Abstract
AbstractThe aim of this contribution is to provide a readable account of Markov Chain Monte Carlo methods, with particular emphasis on their relations with the numerical integration of deterministic and stochastic differential equations. The exposition is largely based on numerical experiments and avoids mathematical technicalities. The presentation is largely self-contained and includes tutorial sections on stochastic processes, Markov chains, stochastic differential equations and Hamiltonian dynamics. The Metropolis Random-Walk algorithm, Metropolis adjusted Langevin algorithm and Hybrid Monte Carlo are discussed in detail, including some recent results.KeywordsMarkov Chain Monte CarloHamiltonian SystemStochastic Differential EquationErgodic TheoremAcceptance ProbabilityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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