Statistics and Computing

, Volume 16, Issue 4, pp 339-354

First online:

DRAM: Efficient adaptive MCMC

  • Heikki HaarioAffiliated withLappeenranta University of Technology Email author 
  • , Marko LaineAffiliated withLappeenranta University of Technology
  • , Antonietta MiraAffiliated withUniversity of Insubria
  • , Eero SaksmanAffiliated withUniversity of Jyväaskyläa

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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 systematic remedy when the adaptation process has a slow start.


Adaptive Markov chain Monte Carlo Adaptive Metropolis-Hastings Delayed rejection Efficiency ordering