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

Autor:	Schmon, Sebastian M, Gagnon, Philippe
Rok vydání:	2021
Předmět:	Statistics - Methodology Statistics - Computation Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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. Comment: Both authors contributed equally. The paper is to appear in Statistics and Computing
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2104.06384 Zobrazit plný text záznamu View this record from Arxiv