The construction of objective priors is, at best, challenging for multidimensional parameter spaces. A common practice is to assume independence and set up the joint prior as the product of marginal distributions obtained via "standard" objective methods, such as Jeffreys or reference priors. However, the assumption of independence a priori is not always reasonable, and whether it can be viewed as strictly objective is still open to discussion. In this paper, by extending a previously proposed objective approach based on scoring rules for the one dimensional case, we propose a novel objective prior for multidimensional parameter spaces which yields a dependence structure. The proposed prior has the appealing property of being proper and does not depend on the chosen model; only on the parameter space considered.

翻译：多维参数空间中客观先验的构建极具挑战性。常见做法是假设各参数独立，并利用"标准"客观方法（如Jeffreys先验或参考先验）获得的边缘分布乘积构建联合先验。然而，先验独立性假设并不总是合理，且其能否被视为严格客观仍存在争议。本文通过将先前基于评分规则的一维客观方法进行扩展，提出了一种新型多维参数空间客观先验，该先验能够产生相依结构。所提先验具有合理性和模型无关性的优良性质，仅依赖于所考虑的参数空间。