This was funny: "You can see how a person who spent too much time in online poker rooms or fantasy baseball thinks they can put odds on the outcomes of elections and other one-off events on their wildly popular blog".
Though I think Nate Silver would say that these are just outcomes from running many simulations of his model, and that the word "probability" is just a shorthand for the fraction of simulations that are true.
I always like to quote Charles Geyer on bootstrapping:
"With ubiquitous fast computing, there is no excuse for not using the bootstrap to improve the accuracy of asymptotics in every serious application. Thus we arrive at the following attitude about asymptotics:
• Asymptotics is only a heuristic. It provides no guarantees.
• If worried about the asymptotics, bootstrap!
• If worried about the bootstrap, iterate the bootstrap!
However, the only justification of the bootstrap is asymptotic. So this leaves us in a quandary of circularity.
• The bootstrap is only a heuristic. It provides no guarantees.
• All justification for the bootstrap is asymptotic!
• In order for the bootstrap to work well, one must bootstrap approximately asymptotically pivotal quantities!"
Awesome article as always, Professor! When thinking about betting, we still have to appeal to some asymptotic notion of probability, right? As the number of times we sample from the outcome distribution goes to infinity, the probability is the proportion of sampled outcomes that have the desired result. Is there any way of quantifying the notion of betting without appealing to infinity like this?
This was funny: "You can see how a person who spent too much time in online poker rooms or fantasy baseball thinks they can put odds on the outcomes of elections and other one-off events on their wildly popular blog".
Though I think Nate Silver would say that these are just outcomes from running many simulations of his model, and that the word "probability" is just a shorthand for the fraction of simulations that are true.
I always like to quote Charles Geyer on bootstrapping:
"With ubiquitous fast computing, there is no excuse for not using the bootstrap to improve the accuracy of asymptotics in every serious application. Thus we arrive at the following attitude about asymptotics:
• Asymptotics is only a heuristic. It provides no guarantees.
• If worried about the asymptotics, bootstrap!
• If worried about the bootstrap, iterate the bootstrap!
However, the only justification of the bootstrap is asymptotic. So this leaves us in a quandary of circularity.
• The bootstrap is only a heuristic. It provides no guarantees.
• All justification for the bootstrap is asymptotic!
• In order for the bootstrap to work well, one must bootstrap approximately asymptotically pivotal quantities!"
source: https://www.stat.umn.edu/geyer/lecam/tr643r.pdf
It's funny that any theory about inductive inference has to be circular question begging.
But he calibrates his model. And so it must match the Vegas odds.
Awesome article as always, Professor! When thinking about betting, we still have to appeal to some asymptotic notion of probability, right? As the number of times we sample from the outcome distribution goes to infinity, the probability is the proportion of sampled outcomes that have the desired result. Is there any way of quantifying the notion of betting without appealing to infinity like this?