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The random walk Metropolis : linking theory and practice through a case study.

By Chris Sherlock, Paul Fearnhead and Gareth Roberts

Abstract

The random walk Metropolis (RWM) is one of the most common Markov Chain Monte Carlo algorithms in practical use today. Its theoretical properties have been extensively explored for certain classes of target, and a number of results with important practical implications have been derived. This article draws together a selection of new and existing key results and concepts and describes their implications. The impact of each new idea on algorithm efficiency is demonstrated for the practical example of the Markov modulated Poisson process (MMPP). A reparameterisation of the MMPP which leads to a highly efficient RWM within Gibbs algorithm in certain circumstances is also developed

Year: 2010
OAI identifier: oai:eprints.lancs.ac.uk:26838
Provided by: Lancaster E-Prints

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Citations

  1. (2001). An adaptive metropolis algorithm.
  2. (2006). An exact Gibbs sampler for the Markov modulated Poisson processes.
  3. (2003). An introduction to MCMC. In: Spatial Statistics and Computational Methods
  4. (2003). Analysis of photon count data from single-molecule fluorescence experiments.
  5. (2005). Bayesian analysis of single-molecule experimental data.
  6. (2009). Bayesian methods for data analysis .
  7. (2009). Bayesian methods for data analysis.
  8. (2007). Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms.
  9. Equations of state calculations by fast computing machine.
  10. (1997). Geometric ergodicity and hybrid Markov chains.
  11. (2005). In discussion of ’Bayesian analysis of single-molecule experimental data’.
  12. (2003). Linking theory and practice of MCMC. In: Highly structured stochastic systems ,
  13. (2003). Linking theory and practice of MCMC. In: Highly structured stochastic systems,
  14. (1996). Markov Chain Monte Carlo in practice.
  15. (2006). Markov chain Monte Carlo. Texts
  16. (1993). Markov chains and stochastic stability . Communications and Control Engineering Series, Springer-Verlag London Ltd.,
  17. (1993). Markov chains and stochastic stability.
  18. (2006). Methodology for inference on the Markov modulated Poisson process and theory for optimal scaling of the random walk Metropolis.
  19. (1997). Monte Carlo methods in statistical mechanics: foundations and new algorithms. In: Functional integration (Carg` ese,
  20. (1997). Monte Carlo methods in statistical mechanics: foundations and new algorithms. In: Functional integration (Carge`se,
  21. (2009). On the containment condition for adaptive Markov chain Monte Carlo algorithms.
  22. (2008). Optimal acceptance rates for Metropolis algorithms: moving beyond 0.234. Stochastic Process.
  23. (2006). Optimal scaling for partially updating MCMC algorithm.
  24. (2001). Optimal scaling for various Metropolis-Hastings algorithms.
  25. (2009). Optimal scaling of the random walk Metropolis on elliptically symmetric unimodal targets. doi
  26. (2002). Polynomial convergence rates of Markov chains.
  27. (1992). Practical Markov chain Monte Carlo.
  28. (2003). The Markov modulated Poisson process and Markov Poisson cascade with applications to web traffic modelling.
  29. (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms. doi
  30. (2007). Weak convergence of Metropolis algorithms for non-i.i.d. target distributions.

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