# 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-