Statistics and Computing

, Volume 16, Issue 4, pp 339–354

DRAM: Efficient adaptive MCMC


    • Lappeenranta University of Technology
  • Marko Laine
    • Lappeenranta University of Technology
  • Antonietta Mira
    • University of Insubria
  • Eero Saksman
    • University of Jyväaskyläa

DOI: 10.1007/s11222-006-9438-0

Cite this article as:
Haario, H., Laine, M., Mira, A. et al. Stat Comput (2006) 16: 339. doi:10.1007/s11222-006-9438-0


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 systematic remedy when the adaptation process has a slow start.


Adaptive Markov chain Monte CarloAdaptive Metropolis-HastingsDelayed rejectionEfficiency ordering

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© Springer Science + Business Media, LLC 2006