Markov chains and Metropolis–Hastings

Content

  • Rejection sampling
  • Basics of Markov chains
  • Metropolis–Hastings algorithm

Learning objectives

At the end of the chapter, students should be able to

  • understand how ordinary Monte Carlo and Markov chain Monte Carlo (MCMC) methods differ
  • implement a MHG algorithm to draw samples from the posterior
  • use output of MCMC to obtain estimates and standard errors
  • use efficient proposals and tuning for MCMC

Readings

Complementary readings

  • Green et al. (2015) (overview of MCMC methods)
  • Neal (2003) (slice sampling)

Slides

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References

Geyer, C. J. (2011). Introduction to Markov chain Monte Carlo. In S. Brooks, A. Gelman, G. Jones, & X. L. Meng (Eds.), Handbook of Markov chain Monte Carlo (pp. 3–48). CRC Press. https://doi.org/10.1201/b10905-3
Green, P. J., Łatuszyński, K., Pereyra, M., & Robert, C. P. (2015). Bayesian computation: A summary of the current state, and samples backwards and forwards. Statistics and Computing, 25(4), 835–862. https://doi.org/10.1007/s11222-015-9574-5
Neal, R. M. (2003). Slice sampling. The Annals of Statistics, 31(3), 705–767. https://doi.org/10.1214/aos/1056562461