摘要翻译：
一个主体关于一个现象的信念的模型可以表现出对称性，即在某些变换下它是不变的。另一方面，这样一个信念模型可能意在表示受试者相信或知道所研究的现象表现出对称性。我们支持这样一种观点，即这些是根本不同的东西，尽管贝叶斯信念模型无法捕捉到这种差异。事实上，未能区分这两种情况导致了拉普拉斯所谓的理由不足原则，该原则在文献中受到了广泛批评。我们表明，有信念模型（不精确概率模型，相干低预见性）推广和包括贝叶斯信念模型，但在那里这种基本的差异可以被捕获。这就引出了这种信念模型的两个对称性概念：弱不变性（表示信念的对称性）和强不变性（模拟对称信念）。我们讨论了这些概念的各种数学以及更多的哲学方面。我们还讨论了几个例子，以表明我们的发现与概率模型和统计推断，特别是与可交换性概念的相关性。
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英文标题：
《Symmetry of models versus models of symmetry》
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作者：
Gert de Cooman and Enrique Miranda
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最新提交年份：
2008
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分类信息：

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：
  A model for a subject's beliefs about a phenomenon may exhibit symmetry, in the sense that it is invariant under certain transformations. On the other hand, such a belief model may be intended to represent that the subject believes or knows that the phenomenon under study exhibits symmetry. We defend the view that these are fundamentally different things, even though the difference cannot be captured by Bayesian belief models. In fact, the failure to distinguish between both situations leads to Laplace's so-called Principle of Insufficient Reason, which has been criticised extensively in the literature.   We show that there are belief models (imprecise probability models, coherent lower previsions) that generalise and include the Bayesian belief models, but where this fundamental difference can be captured. This leads to two notions of symmetry for such belief models: weak invariance (representing symmetry of beliefs) and strong invariance (modelling beliefs of symmetry). We discuss various mathematical as well as more philosophical aspects of these notions. We also discuss a few examples to show the relevance of our findings both to probabilistic modelling and to statistical inference, and to the notion of exchangeability in particular.
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PDF链接：
https://arxiv.org/pdf/801.1966