Stephen Wolfram plays the role of Salonnière in this new, ongoing series of intellectual explorations with special guests.
Power laws, extremely simplified.
We saw that 1) many metrics are stochastic, 2) what is stochastic can be hacked. This is the simplification of my work showing that “p-values are not p-values”, i.e. highly sample dependent, with a skewed distribution. For instance, for a “true” P value of .11, 53% of observations will show less than .05. This allows for hacking: in a few trials, a researcher can get a fake p-value of .01.
Paper is here and in Chapter 19 of SCOFT (Statistical Conseq of Fat Tails): Link to paper – A Short Note on P-Value Hacking
Everything in empirical science is based on the law of large numbers. Remember that it fails under fat tails.
What are Fat Tails? This is very introductory. See the whole book (gets technical beyond Chapter 5)
You can get English subtitles by:
Step 1. Click on Settings (gear icon), Subtitles/CC and select French (auto-generated).
Step 2. Go to Settings again, Subtitles/CC and then select Auto-translate and then select English.
It should then show as “Subtitles/CC (2) French (auto-generated) >> English“
Modern financial theory assumes that distributions are elliptical. We show what happens if the assumption doesn’t hold. And the assumption doesn’t hold.
Diversification does NOT reduce risks in the financial market; it causes near-certain long term blowups under any leverage.
Pasquale Cirillo & Nassim Nicholas Taleb
The COVID-19 pandemic has been a sobering reminder of the extensive damage brought about by epidemics, phenomena that play a vivid role in our collective memory, and that have long been identified as significant sources of risk for humanity. The use of increasingly sophisticated mathematical and computational models for the spreading and the implications of epidemics should, in principle, provide policy- and decision-makers with a greater situational awareness regarding their potential risk. Yet most of those models ignore the tail risk of contagious diseases, use point forecasts, and the reliability of their parameters is rarely questioned and incorporated in the projections. We argue that a natural and empirically correct framework for assessing (and managing) the real risk of pandemics is provided by extreme value theory (EVT), an approach that has historically been developed to treat phenomena in which extremes (maxima or minima) and not averages play the role of the protagonist, being the fundamental source of risk. By analysing data for pandemic outbreaks spanning over the past 2500 years, we show that the related distribution of fatalities is strongly fat-tailed, suggesting a tail risk that is unfortunately largely ignored in common epidemiological models. We use a dual distribution method, combined with EVT, to extract information from the data that is not immediately available to inspection. To check the robustness of our conclusions, we stress our data to account for the imprecision in historical reporting. We argue that our findings have significant implications, including on the extent to which compartmental epidemiological models and similar approaches can be relied upon for making policy decisions.
Link to the Paper – Tail risk of contagious diseases
For n observations, what is the hidden moment? What are you missing from the “empirical” distribution?
Say the maximum flood was 3 meters or maximum loss was 22%. What are we missing in the statistical properties?
Link to the Paper mentioned in the video – What You See and What You Don’t See: The Hidden Moments of a Probability Distribution
Never produce a point estimate for risk management, esp. in a fat-tailed domain, rather show statistical properties. Never judge a risk management stance from point forecasts.