Monte Carlo methods

Content

  • Monte Carlo methods: rejection sampling, importance sampling
  • Basics of Markov chains

Learning objectives

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

  • simulate from target distribution using rejection sampling
  • estimate integrals using importance sampling
  • explain under which circumstances can Markov chain output can be used in place of independent Monte Carlo
  • calculate standard errors for sample means of Markov chain
  • understand the inefficiency due to autocorrelation of Monte Carlo integration based on draws from Markov chains.

Readings

Complementary readings

  • Green et al. (2015) (overview of MCMC methods)

Slides

 View all slides in new window  Download PDF of all slides

Code

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