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.
翻译:高维限定理学已被证明有助于为在随机行进大都会算法中找到最佳比例制定调整规则。 证明趋同效果微弱的假设是限制性的: 目标密度通常被假定为一种产品形式。 因此用户可能怀疑这种调整规则在实际应用中的正确性。 在本文中,我们从不同的角度,即大抽样的角度对最佳比例问题做了一些说明。 这样就可以在现实假设下证明趋同结果不力,并提出新的参数分解调制准则。 在目标密度接近于产品形式时,拟议的准则与以前的准则是一致的,结果突出表明,如果情况并非如此,则必须说明相关结构,以避免性能恶化,同时说明使用自然(不精确的)近似于可用于首次算法运行的关联矩阵的理由。