Abstract
While many of the MCMC algorithms presented in the previous chapter are both generic and universal, there exists a special class of MCMC algorithms that are more model dependent in that they exploit the local conditional features of the distributions to simulate. Before starting the general description of such algorithms, gathered under the (somewhat inappropriate) name of Gibbs sampling, we provide in this chapter a simpler introduction to these special kind of MCMC algorithms. We reconsider the fundamental theorem of simulation (Theorem 2.15) in light of the possibilities opened by MCMC methodology and construct the corresponding slice sampler.
He’d heard stories that shredded documents could be reconstructed. All it took was patience: colossal patience.
—Ian Rankin, Let it Bleed
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Notes
Neal, R. (1997). Markov chain Monte Carlo methods based on “slicing” the density function. Technical report, Univ. of Toronto.
Neal, R. (2003). Slice sampling (with discussion). Ann. Statist., 31: 705–767.
Mira, A., Moller, J., and Roberts, G. (2003). Perfect slice samplers. J. Royal Statist. Soc. Series B, 63: 583–606.
Roberts, G. and Rosenthal, J. (2003). The polar slice sampler. Stochastic Models, 18: 257–236.
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© 2004 Springer Science+Business Media New York
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Robert, C.P., Casella, G. (2004). The Slice Sampler. In: Monte Carlo Statistical Methods. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4145-2_8
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DOI: https://doi.org/10.1007/978-1-4757-4145-2_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1939-7
Online ISBN: 978-1-4757-4145-2
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