Abstract
This chapter is the first of a series on simulation methods based on Markov chains. However, it is a somewhat strange introduction because it contains a description of the most general algorithm of all. The next chapter (Chapter 8) concentrates on the more specific slice sampler, which then introduces the Gibbs sampler (Chapters 9 and 10), which, in turn, is a special case of the Metropolis–Hastings algorithm. (However, the Gibbs sampler is different in both fundamental methodology and historical motivation.)
“What’s changed, except what needed changing?” And there was something in that, Cadfael reflected. What was changed was the replacement of falsity by truth... Ellis Peter, The Confession of Brother Haluin
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Robert, C.P., Casella, G. (2004). The Metropolis—Hastings Algorithm. In: Monte Carlo Statistical Methods. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4145-2_7
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