reversible jump MCMC
(35 minutes to learn)
Summary
Reversible jump MCMC is a special case of Metropolis-Hastings where proposals are made between continuous spaces of differing dimensionality. The most common use is in Bayesian model averaging.
Context
This concept has the prerequisites:
- Bayesian model averaging (Reversible jump MCMC is intended for Bayesian model averaging.)
- Metropolis-Hastings algorithm (Reversible jump MCMC is a special case of Metropolis-Hastings.)
- PDFs of functions of random variables (Deriving the M-H acceptance probability requires computing the PDF of a transformation.)
Goals
- Understand why generic MCMC operators aren't applicable when sampling over spaces of differing dimensionality.
- Know the basic idea behind reversible jump: augmenting the parameter spaces so that they are equal dimension.
- Derive the acceptance probability for the proposal. The tricky part is dealing with the fact that part of the proposal distribution is deterministic.
Core resources (read/watch one of the following)
-Paid-
→ Monte Carlo Strategies in Scientific Computing (2001)
A monograph on Monte Carlo methods.
Location:
Section 5.6, "Reversible jumping rule," pages 122-124
Other notes:
- This covers the special case where the proposals add or delete parameters.
→ Monte Carlo Statistical Methods (2005)
A monograph on Monte Carlo methods.
- Section 11.2.1, "Green's algorithm," pages 429-432
- Section 11.2.2, "A fixed dimension reassessment," pages 432-433
Other notes:
- Don't worry about the measure theoretic terminology.
→ The Bayesian Choice
A graduate-level textbook on Bayesian statistics.
Location:
Section 7.3.4, "Reversible jump MCMC," pages 363-366
See also
-No Additional Notes-