Gibbs sampling block updating

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The goal of this paper is to demystify the analysis that leads to honest answers to (Q1) and (Q2).

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In this paper, we explain exactly what drift and minorization are as well as how and why these conditions can be used to form rigorous answers to (Q1) and (Q2). The results of Rosenthal (1995) and Roberts and Tweedie (1999) allow one to use drift and minorization conditions to construct a formula giving an analytic upper bound on the distance to stationarity.

Andrew Gelman has announced the release of Stan version 1.0.0 and its R interface RStan.

Stan – named after Stanislaw Ulam, the inventor of the Monte Carlo method – is a new MCMC program that represents a major technological leap forward.

Geometric ergodicity of the underlying Markov chain implies that there are central limit theorems available for ergodic averages (Chan and Geyer 1994).

The regenerative simulation technique (Mykland, Tierney and Yu 1995, Robert 1995) can be used to get a consistent estimate of the variance of the asymptotic nor... We introduce a powerful and flexible MCMC algorithm for stochastic simulation.

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