Thread by @AnthonyLeeZhang

I sort of agree with this, but one can flip the question on its head. "Black swan" events are those such that the tools of probability and statistics just don't work well. But why should we expect the universe to be well-described by probability and statistics?

https://twitter.com/vgr/status/1418009793470468098

Pascal's wager essentially says, there is a God or there isn't. It's an individual event. Is it ultimately useful to think about things in terms of there being 1 or 0.1 or 0.0001 or 10^-10 probability of God existing?

Obviously silly example, but applies to:

- Probability of financial crises, hyperinflation
- Global warming-induced apocalypses
- World war

And other long-tail events. Ultimately, it happens or it doesn't. Is it useful to think in terms of probabilities?

"But Bayesian utility maximization requires us to assume a prior and optimize", etc! No non-Bayesian decision-rules are admissible! Decision theory shows that if you are "rational", you "believe" in probabilities!

Sure, but ultimately what you are optimizing, when you put a probability on global warming-induced apocalypses, is total expected utility across a large set of approximately independent alternative universes. Does this ultimately matter, if we only inhabit one of them?

I am slightly joking throughout, but let me illustrate a set of cases where probabilities _do_ make a difference.

- A baseball/basketball/tennis player will tend to win more games if she makes plays with higher probabilities of success

- A business will tend to do well if it launches a bunch of products with higher % of success
- A hedge fund will tend to do well if it does a bunch of trades with high Sharpe
- I will tend to get tenure if I write a bunch of papers with high pub probability

IMO, probabilities make the most meaningful predictions in cases where there are _many approximately independent events_. This describes many cases in the real world!

Probability theory then makes useful predictions about the _precise_ thing that will happen when you draw a lot of times. If you win each point in tennis with 55% probability, you win the game, like, all the time

But for a large fraction of the useful world, there just aren't very many independent draws. We live in an era that likes thinking about things in probabilities. Prediction markets, forecasts, etc. abound and drive many decisions

But ultimately, is it useful to apply these tools in settings where there isn't enough independence for probability to make sharp predictions?

One other thing is that probability and statistics are very young, both in terms of their math development, and their importance in society. I really like this book going through the history and development of probabilistic/statistical thinking

amazon.com/dp/B00BV6RTUG