This paper establishes the asymptotic consistency of the loss‐calibrated variational Bayes (LCVB) method. LCVB is a method for approximately computing Bayesian posterior approximations in a “loss aware” manner. This methodology is also highly relevant in general data‐driven decision‐making contexts. Here, we establish the asymptotic consistency of both the loss‐ calibrated approximate posterior and the resulting decision rules. We also establish the asymptotic consistency of decision rules obtained from a “naive” two‐stage procedure that first computes a standard variational Bayes approximation and then uses this in the decision‐making procedure.

中文翻译：

---

损失校准变分贝叶斯的渐近一致性

本文建立了损失校准变分贝叶斯（LCVB）方法的渐近一致性。LCVB是一种以“损失感知”方式近似计算贝叶斯后验近似的方法。这种方法在一般数据驱动的决策环境中也非常相关。在这里，我们建立了经过损失校正的近似后验和由此产生的决策规则的渐近一致性。我们还建立了从“幼稚”的两阶段过程中获得的决策规则的渐近一致性，该过程首先计算标准的变分贝叶斯近似值，然后在决策过程中使用它。