# Informed reversible jump algorithms

arXiv: https://arxiv.org/abs/1911.02089 · HTML: https://mlsanity.com/paper/1911.02089/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2019.

## Built on by (most cited first, 4 of 4)

- [Transport Reversible Jump Proposals](https://mlsanity.com/paper/2210.12572/) (2022)
- [Improving multiple-try Metropolis with local balancing](https://mlsanity.com/paper/2211.11613/) (2022)
- [Optimal scaling of random-walk Metropolis algorithms using Bayesian large-sample asymptotics](https://mlsanity.com/paper/2104.06384/) (2021)
- [A Novel Framework Using Variational Inference with Normalizing Flows to Train Transport Reversible Jump Proposals](https://mlsanity.com/paper/2512.12742/) (2025)

## Abstract (arXiv)

Incorporating information about the target distribution in proposal mechanisms generally produces efficient Markov chain Monte Carlo algorithms (or at least, algorithms that are more efficient than uninformed counterparts). For instance, it has proved successful to incorporate gradient information in fixed-dimensional algorithms, as seen with algorithms such as Hamiltonian Monte Carlo. In trans-dimensional algorithms, Green (2003) recommended to sample the parameter proposals during model switches from normal distributions with informative means and covariance matrices. These proposal distributions can be viewed as asymptotic approximations to the parameter distributions, where the limit is with regard to the sample size. Models are typically proposed using uninformed uniform distributions. In this paper, we build on the approach of Zanella (2020) for discrete spaces to incorporate information about neighbouring models. We rely on approximations to posterior model probabilities that are asymptotically exact. We prove that, in some scenarios, the samplers combining this approach with that of Green (2003) behave like ideal ones that use the exact model probabilities and sample from the correct parameter distributions, in the large-sample regime. We show that the implementation of the proposed samplers is straightforward in some cases. The methodology is applied to a real-data example. The code is available online.