Table 5.

Taleb’s main statements and our responses.

Forecasting single variables in fat tailed domains is in violation of both common sense and probability theory.	Serious statistical modelers (whether frequentist or Bayesian) would never rely on point estimates to summarize a skewed distribution. Using data as part of a decision process is not a violation of common sense, irrespective of the distribution of the random variable. Possibly using only data and ignoring what is previously known (or expert opinion or physical models) may be unwise in small data problems. We advocate a Bayesian approach, incorporating different sources of information into a logically consistent fully probabilistic model.  We agree that higher order moments (or even the first moment in the case of the Cauchy distribution)  do not exist for certain distributions. This does not preclude making probabilistic statements such as P(a<X<B).
Pandemics are extremely fat tailed.	Yes, and so are many other phenomena. The distribution of financial rewards from mining activity, for example, is incredibly fat tailed and very asymmetric. As such, it is important to accurately quantify the entire distribution of forecasts.  From a Bayesian perspective, we can rely on the posterior distribution (as well as the posterior predictive distribution) as the basis of statistical inference and prediction (Tanner, 1996).
Science is not about making single points predictions but understanding properties (which can sometimes be tested by single points).	We agree and that is why the focus should be on the entire predictive distribution, and why we should be flexible in the way in which we model and estimate this distribution. Bayesian hierarchical models (which can be formulated to account for fat tails, if need be) may allow using all available sources of information in a logically consistent fully probabilistic model.
Risk management is concerned with tail properties and distribution of extrema, not averages or survival functions.	Quality data and calibrated (Bayesian) statistical models may be useful in estimating the behaviour of a random variable across the whole spectrum of outcomes, not just point estimates of summary statistics.  While the three parameter Pareto distribution can be developed based on interesting mathematics, it is not clear that it will provide a measurably better fit to skewed data (e.g. pandemic data in ref. 19) than would a two parameter Gamma distribution fitted to the log counts.  It is certainly not immediately obvious how to generalize either skewed distribution to allow for the use of all available sources of information in a logically consistent fully probabilistic model. In this regard, we note that upon examining the NY daily death count data studied in (Chin et al., 2020b), these data are found to be characterized as stochastic rather than chaotic. (Toker et al., 2000)
Naive fortune cookie evidentiary methods fail to work under both risk management and fat tails as absence of evidence can play a large role in the properties.	A passenger may well get off the plane if it is on the ground and the skills of the pilot are in doubt, but what if he awakes to find he is on a nonstop from JFK to LAX? The poor passenger can stay put, cross her/his fingers, say a few prayers, or can get a parachute and jump; assuming s/he is able and willing to open the exit door in midflight. The choice is not so easy when there are considerable risks associated with either decision that need to be made in real time. We argue that acquiring further information on the pilot’s skill level, perhaps from the flight attendant as s/he strolls down the aisle with the tea trolley, as well as checking that the parachute under the seat (if available) has no holes, would be prudent courses of action. This is exactly the situation that faced New York- they did not arrange to be ground zero of the COVID-19 pandemic in the US. Various models forecast very high demand for ICU beds in New York state. As a result of this forecast, a decision was made to send COVID-19 patients to nursing homes, with tragic consequences.