未来的尾巴比过去粗：模型误差是分支 反事实

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摘要翻译：
事前预测结果应解释为反事实（潜在历史），误差为结果之间的差值。重新应用关于估计误差的不确定度的测量结果会导致分支反事实。这种认知不确定性的递归具有明显不同于传统抽样误差的分布性质。错误率的嵌套反事实总是导致肥尾，不管所使用的概率分布如何，并在某些条件下导致幂律。关于STD的分支错误率仅为0.01%（本身为错误率），而关于该错误率的分支错误率为0.01%等（一路递归）导致爆炸性（和无限大）高于1的矩。缺少任何程度的回归都会导致对小概率和凹收益的低估（福岛就是一个标准例子）。本文阐述了高阶不确定性率（用反事实的差值表示）改变最终分布形状的条件，并说明了接受常规概率方法（细尾或微肥尾）的可靠性需要对背景事实的先验信念。
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英文标题：
《The Future Has Thicker Tails than the Past: Model Error As Branching
  Counterfactuals》
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作者：
Nassim N. Taleb
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最新提交年份：
2012
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
--

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英文摘要：
  Ex ante forecast outcomes should be interpreted as counterfactuals (potential histories), with errors as the spread between outcomes. Reapplying measurements of uncertainty about the estimation errors of the estimation errors of an estimation leads to branching counterfactuals. Such recursions of epistemic uncertainty have markedly different distributial properties from conventional sampling error. Nested counterfactuals of error rates invariably lead to fat tails, regardless of the probability distribution used, and to powerlaws under some conditions. A mere .01% branching error rate about the STD (itself an error rate), and .01% branching error rate about that error rate, etc. (recursing all the way) results in explosive (and infinite) higher moments than 1. Missing any degree of regress leads to the underestimation of small probabilities and concave payoffs (a standard example of which is Fukushima). The paper states the conditions under which higher order rates of uncertainty (expressed in spreads of counterfactuals) alters the shapes the of final distribution and shows which a priori beliefs about conterfactuals are needed to accept the reliability of conventional probabilistic methods (thin tails or mildly fat tails).
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PDF链接：
https://arxiv.org/pdf/1209.2298

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关键词：Conventional Applications distribution Measurements Quantitative 常规 tails 导致 回归 rate