标题： 关于先验接近无知下的类别潜在变量的学习 显示英文标题

标题： Learning about a Categorical Latent Variable under Prior Near-Ignorance

摘要： 众所周知，完全的先验无知与学习是不相容的，至少在（认识论）不确定性的连贯理论中是这样。鲜为人知的是，存在一种类似于完全无知的状态，沃尔利称之为近似无知，它允许学习的发生。 在本文中，我们提供了新的且大量的证据，表明即使是在接近无知的情况下，也无法真正被视为解决在非常弱的信念条件下开始统计推断问题的方法。 这一结果的关键在于关注一个由感兴趣的潜变量所定义的情境。我们认为这种情境在实践中是最常见的，并且我们展示了，对于分类潜变量（以及一般显变量）的情况，有一个充分条件，如果满足该条件，则在先验近似无知的情况下无法进行学习。 我们还表明，这个条件在最常见的统计问题中很容易得到满足。 显示英文摘要

摘要： It is well known that complete prior ignorance is not compatible with learning, at least in a coherent theory of (epistemic) uncertainty. What is less widely known, is that there is a state similar to full ignorance, that Walley calls near-ignorance, that permits learning to take place. In this paper we provide new and substantial evidence that also near-ignorance cannot be really regarded as a way out of the problem of starting statistical inference in conditions of very weak beliefs. The key to this result is focusing on a setting characterized by a variable of interest that is latent. We argue that such a setting is by far the most common case in practice, and we show, for the case of categorical latent variables (and general manifest variables) that there is a sufficient condition that, if satisfied, prevents learning to take place under prior near-ignorance. This condition is shown to be easily satisfied in the most common statistical problems.