Score-driven models update time-varying parameters using conditional likelihood scores. This paper gives a Bayesian interpretation based on Tweedie's formula. In Gaussian signal extraction, Tweedie's formula expresses the posterior correction as a scaled score of the marginal predictive density; in natural exponential families, the corresponding identity includes a base-measure adjustment. For general conditional densities, we show that inverse-Fisher-scaled conditional scores arise as local Gaussian posterior corrections based on Fisher scoring and precision discounting. For conjugate natural exponential families, the classical discounted Bayesian recursion has an exact score-driven representation: with steady-state precision discounting and expectation-space inverse-Fisher scaling, the score-driven correction equals the Bayesian posterior mean before transition dynamics are imposed. Tweedie's variance-function index further clarifies how conditional scores normalize forecast errors. The results link empirical Bayes, approximate filtering, dynamic generalized linear models, and score-driven models while distinguishing exact Bayesian updating from local score-based approximation.

翻译：得分驱动模型利用条件似然得分更新时变参数。本文基于特威迪公式给出贝叶斯解释。在高斯信号提取中，特威迪公式将后验修正表示为边际预测密度的缩放得分；在自然指数族中，相应恒等式包含基测度调整项。针对一般条件密度，我们证明：基于费舍尔评分和精度贴现的局部高斯后验修正，可导出逆费舍尔缩放的条件得分。对于共轭自然指数族，经典贴现贝叶斯递归具有精确的得分驱动表示：在稳态精度贴现和期望空间逆费舍尔缩放下，得分驱动修正等于施加转移动力学前的贝叶斯后验均值。特威迪方差函数指数进一步阐明了条件得分如何归一化预测误差。这些结果连接了经验贝叶斯、近似滤波、动态广义线性模型和得分驱动模型，同时区分了精确贝叶斯更新与基于局部得分的近似方法。