Score-driven models update time-varying parameters using conditional likelihood scores. This paper develops a Bayesian interpretation of such updates through Tweedie's formula, which connects posterior mean corrections with marginal scores. In Gaussian signal extraction, this gives an exact posterior-correction identity. For natural exponential families, related identities characterize posterior means in natural- and expectation-parameter spaces. Building on these identities, we show that conjugate Bayesian filtering in expectation space coincides exactly with an inverse-Fisher-scaled conditional score update under local precision discounting. For general conditional densities, the exact Bayesian correction involves a generally unavailable predictive-marginal score. A local Gaussian approximation shows that the conditional likelihood score provides the leading approximation to this posterior correction; under local precision discounting, the predictive covariance becomes proportional to inverse Fisher information, yielding the familiar inverse-Fisher-scaled score recursion. The results clarify when score-driven updates are exact Bayesian filters and when they should instead be viewed as tractable local approximations.

翻译：得分驱动模型通过条件似然得分更新时变参数。本文利用Tweedie公式为这类更新建立贝叶斯解释，该公式将后验均值修正与边际得分联系起来。在高斯信号提取中，这给出了精确的后验修正恒等式。对于自然指数族，相关恒等式刻画了自然参数空间与期望参数空间中的后验均值。基于这些恒等式，我们证明：在局部精度折扣条件下，期望空间中的共轭贝叶斯滤波与逆费舍尔标度的条件得分更新完全一致。对于一般条件密度，精确的贝叶斯修正涉及通常不可获得的预测边际得分。局部高斯近似表明，条件似然得分提供了该后验修正的主阶近似；在局部精度折扣条件下，预测协方差与逆费舍尔信息成正比，从而得到熟悉的逆费舍尔标度得分递归。上述结果阐明了得分驱动更新在何种情况下是精确的贝叶斯滤波，在何种情况下应视为可处理的局部近似。