当无知是幸福
When Ignorance is Bliss
摘要：
人们普遍认为，信息越多越好，信息永远不应该被忽视。在这里，我们认为，使用贝叶斯和非贝叶斯分析，在某些情况下，你最好忽略信息，如果你的不确定性是由一组概率测量。这些包括信息与手头的预测任务相关的情况。在非贝叶斯分析中，我们展示了忽略信息如何避免膨胀，这种现象是额外的信息有时会导致不确定性增加。在贝叶斯分析中，我们表明，对于小样本量和某些预测任务，基于无信息先验的贝叶斯后验比简单地忽略给定的信息产生更差的预测。
英文摘要：
It is commonly-accepted wisdom that more information is better, and that information should never be ignored. Here we argue, using both a Bayesian and a non-Bayesian analysis, that in some situations you are better off ignoring information if your uncertainty is represented by a set of probability measures. These include situations in which the information is relevant for the prediction task at hand. In the non-Bayesian analysis, we show how ignoring information avoids dilation, the phenomenon that additional pieces of information sometimes lead to an increase in uncertainty. In the Bayesian analysis, we show that for small sample sizes and certain prediction tasks, the Bayesian posterior based on a noninformative prior yields worse predictions than simply ignoring the given information.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
