摘要翻译：
众所周知，完全的先验无知与学习是不相容的，至少在一个关于（认知）不确定性的连贯理论中是如此。不太为人所知的是，有一种类似于完全无知的状态，Walley称之为近乎无知，这种状态允许学习发生。在本文中，我们提供了新的和实质性的证据，证明在信念非常弱的条件下，也不能真的把近乎无知看作是摆脱开始统计推断问题的一种方法。这一结果的关键是关注一个以潜在的感兴趣的变量为特征的设置。我们争辩说，这种设置是实践中最常见的情况，并且我们表明，对于范畴潜在变量（和一般显化变量）的情况，有一个充分条件，如果得到满足，就会阻止学习在先前的近乎无知的情况下发生。这个条件在最常见的统计问题中很容易得到满足。
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英文标题：
《Learning about a Categorical Latent Variable under Prior Near-Ignorance》
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作者：
Alberto Piatti and Marco Zaffalon and Fabio Trojani and Marcus Hutter
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/705.4312