This paper presents a novel method for analytical derivations of marginal densities using the fractional derivatives of moment-generating functions. Although the method requires likelihood functions to take specific forms, its assumptions are otherwise modest. It only requires that the prior moment-generating functions exist, are finite, and are continuous and differentiable at certain points. We also present the probabilistic and statistical insights behind this method.

翻译：本文提出了一种利用矩生成函数的分数阶导数解析推导边际密度的新方法。尽管该方法要求似然函数具有特定形式，但其假设条件相对宽松。该方法仅要求先验矩生成函数存在、有限，并在特定点处连续且可导。我们还阐述了该方法背后的概率与统计洞见。