Incerto 4-Book Bundle: Fooled by Randomness, The Black Swan, The Bed of Procrustes, Antifragile

by Nassim Nicholas Taleb

The problem of the circularity of statistics (which we can also call the statistical regress argument) is as follows. Say you need past data to discover whether a probability distribution is Gaussian, fractal, or something else. You will need to establish whether you have enough data to back up your claim. How do we know if we have enough data? From the probability distribution—a distribution does tell you whether you have enough data to “build confidence” about what you are inferring. If it is a Gaussian bell curve, then a few points will suffice (the law of large numbers once again). And how do you know if the distribution is Gaussian? Well, from the data. So we need the data to tell us what the probability distribution is, and a probability distribution to tell us how much data we need. This causes a severe regress argument.