# Optimal scaling of random-walk Metropolis algorithms using Bayesian large-sample asymptotics

arXiv: https://arxiv.org/abs/2104.06384 · HTML: https://mlsanity.com/paper/2104.06384/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 41 references that are in the map.
- First posted on arXiv 13 Apr 2021.

## Builds on (most cited first, 2 of 2)

- [Informed reversible jump algorithms](https://mlsanity.com/paper/1911.02089/) (2019)
- [An automatic robust Bayesian approach to principal component regression](https://mlsanity.com/paper/1711.06341/) (2017)

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

- [Black-box Bayesian inference for economic agent-based models](https://mlsanity.com/paper/2202.00625/) (2022)
- [Approximate Bayesian Computation with Path Signatures](https://mlsanity.com/paper/2106.12555/) (2021)
- [Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation](https://mlsanity.com/paper/2202.11585/) (2022)
- [Improving multiple-try Metropolis with local balancing](https://mlsanity.com/paper/2211.11613/) (2022)

## Abstract (arXiv)

High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the target density is typically assumed to be of a product form. Users may thus doubt the validity of such tuning rules in practical applications. In this paper, we shed some light on optimal-scaling problems from a different perspective, namely a large-sample one. This allows to prove weak convergence results under realistic assumptions and to propose novel parameter-dimension-dependent tuning guidelines. The proposed guidelines are consistent with previous ones when the target density is close to having a product form, and the results highlight that the correlation structure has to be accounted for to avoid performance deterioration if that is not the case, while justifying the use of a natural (asymptotically exact) approximation to the correlation matrix that can be employed for the very first algorithm run.