#### Nassim Nicholas Taleb (Scholar Investor) – Tail risk of contagious diseases (May 2020)

#### Chapters

#### Abstract

The Intricacies of Statistical Analysis and Policy Implications in Understanding Extreme Events

Abstract

The rapidly evolving field of statistical analysis, particularly in the context of understanding and managing extreme events, has recently highlighted the criticality of employing robust methodologies and the dire consequences of underestimating risks in policy decisions. This article explores various aspects of statistical techniques such as reliability testing, aberration removal, power law exponent analysis, and extreme value theory, alongside the implications of these methodologies in policy-making and historical understanding. It also discusses the challenges in statistical education and the importance of interdisciplinary collaboration in comprehending complex phenomena.

Main Ideas and Importance

1. Reliability Testing and Robustness of Results: Emphasizing the consistency of parameters even under varying conditions, indicating the robustness of statistical results.

2. Aberration Removal Methods: Highlighting the stability of outcomes post aberration removal, ensuring data accuracy.

3. Power Law Exponent Analysis: The significance of the alpha value in indicating heavy tails in data distribution.

4. Extreme Value Theory in Pandemic Analysis: Utilizing extreme value theory to analyze pandemic data, addressing challenges with bounded random variables.

5. Phi Transformation in Statistical Analysis: Implementing transformations to manage unbounded variables, allowing for more accurate statistical modeling.

6. Handling Incomplete Historical Data: Overcoming the challenges of unreliable historical data by focusing on distribution tails.

7. EVT and Semi-Parametric Approach: Combining EVT with flexible modeling techniques to better understand extreme events.

8. Policy Implications of Statistical Analysis: Stressing the importance of considering extreme events in policy-making, rather than relying solely on point estimates.

9. Technical Considerations in Historical Pandemic Data: Recognizing the incompleteness of historical data while maintaining robust analysis.

10. Methodological Considerations in Fat-tailed Distributions: Understanding the informational shift towards distribution tails in fat-tailed distributions.

11. Historical Consistency in War Observations: The reliability of historical war data in understanding extreme events.

12. The Necessity of Early Action in Outbreaks: Drawing lessons from historical practices in managing outbreaks.

13. Rational Reaction versus Paranoia in Pandemic Assessment: Differentiating between rational reaction and paranoia in pandemic risk assessment.

14. Size Fallacy in Statistical Comparison: Warning against inappropriate comparisons between different distribution classes.

15. Historical Neglect of Extreme Value Theory: Addressing the limited awareness of extreme value theory outside specialized communities.

16. Value of Interdisciplinary Collaboration: The critical role of interdisciplinary collaboration in understanding complex phenomena.

17. Challenges in Traditional Statistics Education: Recognizing the limitations of traditional statistics education, especially in fields dealing with power law distributions.

18. Importance of Pre-Asymptotic Behavior in Real-world Phenomena: Acknowledging the non-Gaussian behavior of many real-world phenomena in their early stages.

19. Reformation in Statistical Education: Advocating for a reformed approach in teaching statistics, focusing on fundamental concepts and their applications.

Expanded Discussion

Reliability Testing and Robustness

The application of multiple time series and repetitive testing underscores the reliability of statistical outcomes. Such methodologies ensure that results are not mere artifacts of specific data sets but rather indicative of a consistent pattern.

Robustness Testing of Power Law Parameters and Extreme Value Theory

To address the unreliability of historical data, the high and low values of observations were used to generate 10,000 time series between the extremes. Parameters of interest were analyzed across these generated series to assess their stability. Aberrations were removed using the jackknife and bootstrap methods. Results remained consistent, indicating the robustness of the alpha parameter. The alpha value for the power law, representing the tail exponent, was consistently below 1, regardless of the method used.

Aberration Removal and Power Law Exponent

The removal of aberrations using advanced techniques like the jackknife and bootstrap methods, along with the analysis of power law exponents, enhances the accuracy and reliability of statistical findings. The consistent alpha value below 1 points to the presence of heavy tails in data distributions, a crucial factor in understanding extreme events.

Extreme Value Theory in Pandemics

Applying extreme value theory to pandemic data presents unique challenges due to the bounded nature of the variables. However, the use of phi transformations facilitates the application of advanced statistical methods, providing a more accurate understanding of pandemic impacts.

Extracting Information from Incomplete Data on Pandemics

The authors developed a new method for analyzing incomplete historical data on pandemics. The method combines extreme value theory and a transformation to extract meaningful statistical properties from the data. The method focuses on the tail of the distribution, which is important for understanding the risk of extreme events. The authors argue that their method provides a more robust way to estimate the risk of pandemics than traditional methods. Historians are often unreliable sources of information, so it is important to be skeptical of their accounts. The authors developed a method for dealing with liars by applying a transformation to the data. The transformation allows us to use the Turing Value Theory to estimate the parameters of the distribution.

Policy Implications

The research underlines the importance of not relying solely on point estimates for policy decisions. Instead, understanding the statistical properties of data and considering the potential for extreme events is vital, especially in risk management fields where overlooking such events can lead to catastrophic outcomes.

Understanding Uncertainty and Fat Tail Distributions in Data Analysis

In statistical analysis, the fatter the tail of a distribution, especially if it’s a one-tailed distribution, the less information is contained in the body of the distribution. This means that even with a trillion data points in the body, a single outlier in the tail can dominate the statistical properties. In the context of large events, such as wars or pandemics, removing or adding observations has minimal impact on the overall statistical analysis. Historians’ potential exaggerations or misrepresentations do not significantly alter the observed patterns. Maxima, or extreme events, are highly informative because they are less likely to be unrecorded. Events like World War II or the Spanish flu are almost certainly documented, making their data valuable for analysis. In the absence of complete certainty about a disease, it is essential to assume a fat-tailed distribution. The number of unrecorded cases of a disease is often unknown, and this uncertainty must be accounted for in policy decisions.

Methodological Considerations and Historical Data

The focus on the tail of data distributions, especially in the context of incomplete historical records, highlights the method’s robustness. This approach allows for meaningful analysis despite data limitations, shifting the focus from the bulk to the extreme ends of distributions.

Robustness of the Results

The authors acknowledge that their data set is incomplete, but they argue that their results are robust. The method focuses on the tail of the distribution, which is less sensitive to missing data. The authors believe that their method provides a more accurate estimate of the risk of pandemics than traditional methods. The method can be used to inform public policy decisions about pandemic preparedness and response.

Early Action and Rational Reaction in Pandemics

Historical perspectives emphasize the need for early and decisive action in managing pandemics, drawing parallels to practices in the Mediterranean region. The discussion also criticizes the dismissal of pandemic concerns as paranoia, advocating for a rational approach based on accurate probability distributions.

Fat Tails and Early Response:

– Nassim Nicholas Taleb emphasizes the importance of taking drastic measures early to contain outbreaks, especially for diseases with fat tails, where extreme events are more likely.

– He highlights that if measures had been taken in January, the situation would be different.

– Pascual Cirillo mentions the historical practice of quarantining ships and shutting down towns upon suspicion of disease, emphasizing the value of early reactions.

Early Response and Paranoia:

– Cirillo criticizes the dismissal of pandemic concerns as paranoia, arguing that a rational approach based on accurate probability distributions is necessary.

– He emphasizes the need for early and decisive action, drawing parallels to historical practices in the Mediterranean region.

Education and Interdisciplinary Collaboration

The article underscores the shortcomings of traditional statistics education and the necessity of rethinking teaching methods. It advocates for an interdisciplinary approach, combining expertise from various fields to fully comprehend complex phenomena.

Challenges in Teaching Statistics:

– Taleb criticizes the teaching of statistics, arguing that it is often not mathematical enough and focuses too much on learning how to cook rather than understanding the underlying principles.

– He emphasizes the need to teach probability before statistics to avoid harmful mistakes.

– Cirillo mentions that fundamental results in extreme value theory were not widely known outside the community of extremists, even among statisticians.

Interdisciplinary Collaboration:

– The article emphasizes the value of interdisciplinary collaboration in understanding complex phenomena, combining expertise from various fields.

– It highlights the importance of integrating statistical methods with knowledge from other disciplines, such as history, sociology, and economics.

Conclusion

The exploration of statistical methodologies in the context of extreme events reveals the complexities and challenges inherent in this field. It emphasizes the need for robust analysis, careful consideration in policy-making, and a reformed approach in education to better prepare for and understand these critical phenomena. The collaboration between various disciplines further enriches this understanding, leading to more comprehensive and effective strategies in managing extreme events.

Notes by: Flaneur