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Bayesian Data Analysis, Third Edition, 3rd Edition by Donald B. Rubin, Aki Vehtari, David B. Dunson, Hal S. Stern, John B. Carlin, Andrew Gelman

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Chapter 12

Computationally efficient Markov chain simulation

The basic Gibbs sampler and Metropolis algorithm can be seen as building blocks for more advanced Markov chain simulation algorithms that can work well for a wide range of problems. In Sections 12.1 and 12.2, we discuss reparameterizations and settings of tuning parameters to make Gibbs and Metropolis more efficient. Section 12.4 presents Hamiltonian Monte Carlo, a generalization of the Metropolis algorithm that includes ‘momentum’ variables so that each iteration can move farther in ...

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