Penalizing complexity (PC) priors is a principled framework for designing priors that reduce model complexity. PC priors penalize the Kullback-Leibler Divergence (KLD) between the distributions induced by a ``simple'' model and that of a more complex model. However, in many common cases, it is impossible to construct a prior in this way because the KLD is infinite. Various approximations are used to mitigate this problem, but the resulting priors then fail to follow the designed principles. We propose a new class of priors, the Wasserstein complexity penalization (WCP) priors, by replacing KLD with the Wasserstein distance in the PC prior framework. These priors avoid the infinite model distance issues and can be derived by following the principles exactly, making them more interpretable. Furthermore, principles and recipes to construct joint WCP priors for multiple parameters analytically and numerically are proposed and we show that they can be easily obtained, either numerically or analytically, for a general class of models. The methods are illustrated through several examples for which PC priors have previously been applied.

翻译：惩罚复杂度（PC）先验是一种设计降低模型复杂度先验的原则性框架。PC先验通过惩罚"简单"模型与复杂模型所诱导分布间的KL散度（KLD）来构建先验。然而在许多常见情况下，由于KLD为无穷大，无法以此方式构建先验。现有研究采用多种近似方法缓解该问题，但由此得到的先验会偏离既定的设计原则。本文提出一类新型先验——Wasserstein复杂度惩罚（WCP）先验，该先验在PC先验框架中用Wasserstein距离替代KLD。这类先验能规避模型距离无穷大的问题，且严格遵循原则推导，因此具有更强的可解释性。进一步地，我们提出了在解析和数值层面构建多参数联合WCP先验的原则与方案，并证明对于一般模型类，这类先验可轻松通过数值或解析方式获得。本文通过多个此前已应用PC先验的案例对该方法进行了验证。