Bayes’ rule, as one of the fundamental concepts of statistical signal processing, provides a way to update our belief about an event based on the arrival of new pieces of evidence. Uncertainty is traditionally modeled by a probability distribution. Prior belief is thus expressed by a prior probability distribution, while the update involves the likelihood function, a probabilistic expression of how likely it is to observe the evidence. It has been argued by many statisticians, however, that a broadening of probability theory is required because one may not always be able to provide a probability for every event, due to the scarcity of training data.

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使用不精确概率的贝叶斯规则 [讲座笔记]

贝叶斯规则作为统计信号处理的基本概念之一，提供了一种根据新证据的出现来更新我们对事件的信念的方法。传统上，不确定性是通过概率分布来建模的。因此，先验信念由先验概率分布表示，而更新涉及似然函数，即观察证据的可能性的概率表达。然而，许多统计学家认为，需要扩大概率论，因为由于训练数据的稀缺，人们可能并不总是能够为每个事件提供概率。