Ignore this post.

distillation of Taleb's core idea:

expected value estimates are dominated by tail events (unless the distribution is thin-tailed)

repeated sampling from a distribution usually does not yield information about tail events

therefore repeated sampling can be used to estimate EVs iff the distribution is thin-tailed according to your priors

if the distribution is fat-tailed according to your priors, how to determine EV?

estimating EV is much harder

some will say to use the sample mean as EV anyway, they are wrong

in the absence of information on tail events (which is v common)

you must judge the fatness of the left/right tails based on your priors

right tail is fat and left is thin: high EV

left tail is fat and right is thin: low EV (/ high magnitude in the negative direction)

both tails are fat: EV is highly uncertain

to reiterate:

when calculating EV of a distribution that you have samples from:

the burden of proof is on you to show that you are operating in a thin-tailed domain

before you use the sample mean as an estimate of EV

else, you must rely on your prior beliefs on the fatness of the tails of the distribution

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Ignore this post.

distillation of Taleb's core idea:expected value estimates are dominated by tail events (unless the distribution is thin-tailed)

repeated sampling from a distribution usually

does notyield information about tail eventstherefore repeated sampling can be used to estimate EVs

iffthe distribution is thin-tailed according to your priorsif the distribution is fat-tailed according to your priors, how to determine EV?

estimating EV is much harder

some will say to use the sample mean as EV anyway, they are wrong

in the absence of information on tail events (which is v common)

you must judge the fatness of the left/right tails based on your priors

right tail is fat and left is thin: high EV

left tail is fat and right is thin: low EV (/ high magnitude in the negative direction)

both tails are fat: EV is highly uncertain

to reiterate:

when calculating EV of a distribution that you have samples from:

the burden of proof is on you to show that you are operating in a thin-tailed domain

beforeyou use the sample mean as an estimate of EVelse, you must rely on your prior beliefs on the fatness of the tails of the distribution