内容简介

The book investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible.

Switching from thin tailed to fat tailed distributions requires more than “changing the color of the dress.” Traditional asymptotics deal mainly with either n=1 or n=∞, and the real world is in between, under the “laws of the medium numbers”–which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence.

A few examples:

- The sample mean is rarely in line with the population mean, with effect on “naïve empiricism,” but can be sometimes be estimated via parametric methods.

- The “empirical distribution” is rarely empirical.

- Parameter uncertainty has compounding effects on statistical metrics.

- Dimension reduction (principal components) fails.

- Inequality estimators (Gini or quantile contributions) are not additive and produce wrong results.

- Many “biases” found in psychology become entirely rational under more sophisticated probability distributions.

- Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions.

This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.

作者简介

Nassim Nicholas Taleb spent 20 years as a derivatives and mathematical trader before starting his second career in applied probability. He is the author of 5-volume Incerto, an essay on uncertainty, published in 40 languages–with parallel journal articles and technical commentaries of which this book is an organized compilation. Taleb is currently Distinguished Professor of Ris...

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精彩摘录

到达时间间隔大型战乱冲突事件的到达时间间隔非常长，近似于齐次泊松过程:所以不存在任何显著的趋势，人类也无法证明自己比先辈更善良。对于导致1000万人伤亡的大型冲突事件(量级稍弱于一战和二战)，其平均时间间隔是136年，平均偏差是267年(或者按今天的人口重整数据，平均时间间隔为52年，平均偏差为61年)。当前70年的“长期和平”显然不足以推测出未来发生第三次世界大战的概率。

——引自章节：第G章第三次世界大战发生的概率有多高？

有时候，人们会引用所谓的“经验”数据来说明我们不该担心埃博拉病毒，因为2016年只有两个美国人死于埃博拉病毒。他们认为，从死亡数字看，我们更应该担心死于糖尿病或躺在床上。但如果我们从尾部的角度思考，假设有一天报纸报道突然死了20亿人，他们更可能死于埃博拉病毒还是死于吸烟、糖尿病或躺在床上呢？

——引自章节：第三章非数理视角概述-剑桥大学达尔文学院讲义