Roberts and Rosenthal (2016) Complexity Bounds for Markov Chain Monte Carlo Algorithms via Diffusion Limits

A Blog Entry on Bayesian Computation by an Applied Mathematician

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概要

(Gareth O. Roberts and Rosenthal, 2016) は (G. O. Roberts et al., 1997), (Gareth O. Roberts and Rosenthal, 1998) で試みられたような最適スケーリングの結果を，アルゴリズムの複雑性に関する結果に換言する方法を議論したもの．

Roberts and Rosenthal (1998) Optimal Scaling of Discrete Approximations to Langevin Diffusions

Roberts and Rosenthal [Journal of the Royal Statistical Society. Series B 60(1998) 255-268] は MALA (Metropolis-Adjusted Langevin Algorithm) の最適スケーリングを論じたもの．

最適スケーリングについては (Gareth O. Roberts and Rosenthal, 2001) も参照．

Roberts and Rosenthal (2001) Optimal Scaling for Various Metropolis-Hastings Algorithms

Roberts and Rosenthal [Statistical Science 16(2001) 351-67] は Metropolis-Hastings 法の最適スケーリングに関する結果をまとめ，実際の実装にその知見をどのように活かせば良いかを例示したレビュー論文である．

References

Roberts, G. O., Gelman, A., and Gilks, W. R. (1997). Weak Convergence and Optimal Scaling of Random Walk Metropolis Algorithms. The Annals of Applied Probability, 7(1), 110–120.

Roberts, Gareth O., and Rosenthal, J. S. (1998). Optimal scaling of discrete approximations to langevin diffusions. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 60(1), 255–268.

Roberts, Gareth O., and Rosenthal, J. S. (2001). Optimal Scaling for Various Metropolis-Hastings Algorithms. Statistical Science, 16(4), 351–367.

Roberts, Gareth O., and Rosenthal, J. S. (2016). Complexity Bounds for Markov Chain Monte Carlo Algorithms via Diffusion Limits. Journal of Applied Probability, 53(2), 410–420.