Springer (part of Springer Nature), Statistics and Computing, 4(16), p. 339-354
DOI: 10.1007/s11222-006-9438-0
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We propose to combine two quite powerful ideas that have recently appeared in the Markov chain Monte Carlo literature: adaptive Metropolis samplers and delayed rejection. The ergodicity of the resulting non-Markovian sampler is proved, and the efficiency of the combination is demonstrated with various examples. We present situations where the combination outperforms the original methods: adaptation clearly enhances efficiency of the delayed rejection algorithm in cases where good proposal distributions are not available. Similarly, delayed rejection provides a sys- tematic remedy when the adaptation process has a slow start.