Rates of convergence of the Hastings and Metropolis algorithms

@article{Mengersen1996RatesOC,
  title={Rates of convergence of the Hastings and Metropolis algorithms},
  author={K. Mengersen and R. Tweedie},
  journal={Annals of Statistics},
  year={1996},
  volume={24},
  pages={101-121}
}
We apply recent results in Markov chain theory to Hastings and Metropolis algorithms with either independent or symmetric candidate distributions, and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution $pi$. In the independence case (in $mathbb{R}^k$) these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of $pi$; in the symmetric case (in $mathbb{R… Expand
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