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Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms

  • Gareth O. Roberts (a1) and Jeffrey S. Rosenthal (a2)
Abstract

We consider basic ergodicity properties of adaptive Markov chain Monte Carlo algorithms under minimal assumptions, using coupling constructions. We prove convergence in distribution and a weak law of large numbers. We also give counterexamples to demonstrate that the assumptions we make are not redundant.

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Copyright
Corresponding author
Postal address: Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YF, UK. Email address: g.o.roberts@lancaster.ac.uk
∗∗ Postal address: Department of Statistics, University of Toronto, Toronto, Ontario, Canada M5S 3G3. Email address: jeff@math.toronto.edu
References
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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