On the use of auxiliary variables inMarkov chain

We study the slice sampler, a method of constructing a reversible Markov chain with a speciied invariant distribution. Given an independence Metropolis-Hastings algorithm it is always possible to construct a slice sampler that dominates it in the Peskun sense. This means that the resulting Markov chain produces estimates with a smaller asymptotic variance. Furthermore the slice sampler has a smaller second-largest eigenvalue than the corresponding independence Metropolis-Hastings algorithm. This ensures faster convergence to the distribution of interest. A suucient condition for uniform er-godicity of the slice sampler is given and an upper bound for the rate of convergence to stationarity is provided.

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