On the Geometric Ergodicity of Metropolis-Hastings Algorithms
نویسنده
چکیده
Abstract Under a compactness assumption, we show that a φ-irreducible and aperiodic MetropolisHastings chain is geometrically ergodic if and only if its rejection probability is bounded away from unity. In the particular case of the Independence Metropolis-Hastings algorithm, we obtain that the whole spectrum of the induced operator is contained in (and in many cases equal to) the essential range of the rejection probability of the chain as conjectured by Liu (1996).
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