最大化从有限数据中学习的信息选择一个简单的模型
Maximizing the information learned from finite data selects a simple model
摘要：
我们使用无信息贝叶斯先验选择的语言来研究选择适当简单的有效模型。我们提倡先验，它最大化参数和预测之间的互信息，尽可能从有限的数据中学习。当许多参数受到可用数据的约束很差时，我们发现这种先验只在参数流形的边界上加权。因此，它选择了一个低维有效的理论在原则上，忽略无关的参数方向。在有足够的数据来严格约束任何数量的参数的极限下，这简化为Jeffreys先验。但我们认为，这种限制是病态的超带状参数流形在科学中通用时，因为它会导致戏剧性的依赖于不可见的实验效果。
英文摘要：
We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by the available data, we find that this prior puts weight only on boundaries of the parameter manifold. Thus it selects a lower-dimensional effective theory in a principled way, ignoring irrelevant parameter directions. In the limit where there is sufficient data to tightly constrain any number of parameters, this reduces to Jeffreys prior. But we argue that this limit is pathological when applied to the hyper-ribbon parameter manifolds generic in science, because it leads to dramatic dependence on effects invisible to experiment.
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