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 the 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.

高维极限定理已被证明可用于导出调整规则，以在随机游走 Metropolis 算法中找到最佳缩放比例。然而，证明弱收敛结果的假设是有限制的：目标密度通常被假设为乘积形式。因此，用户可能会怀疑这种调整规则在实际应用中的有效性。在本文中，我们从不同的角度（即大样本角度）阐明了最优缩放问题。这可以证明现实假设下的弱收敛结果，并提出新颖的参数维度相关的调整指南。当目标密度接近产品形式时，所提出的指南与之前的指南一致，结果强调必须考虑相关结构以避免性能恶化（如果情况并非如此），同时证明使用相关矩阵的自然（渐近精确）近似，可用于第一次算法运行。