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1 results

  • A note on acceptance rate criteria for CLTS for Metropolis–Hastings algorithms

  • Part of
  • G. O. Roberts
  • Journal:
    Journal of Applied Probability / Volume 36 / Issue 4 / December 1999
    Published online by Cambridge University Press:
    14 July 2016, pp. 1210-1217
    Print publication:
    December 1999

  • This paper considers positive recurrent Markov chains where the probability of remaining in the current state is arbitrarily close to 1. Specifically, conditions are given which ensure the non-existence of central limit theorems for ergodic averages of functionals of the chain. The results are motivated by applications for Metropolis–Hastings algorithms which are constructed in terms of a rejection probability (where a rejection involves remaining at the current state). Two examples for commonly used algorithms are given, for the independence sampler and the Metropolis-adjusted Langevin algorithm. The examples are rather specialized, although, in both cases, the problems which arise are typical of problems commonly occurring for the particular algorithm being used.