If you think you can beat the American __ Association over a long run average, that's great news for you! That means free money!
Being right is super valuable, and you should monetize it immediately.
Anything else is just hot air.
Lots of Bayes fans, but can't seem to define what Bayes is.
Since Bayes theorem is a reformulation of the chain rule, anything that is probabilistic "uses Bayes theorem" somewhere, including all frequentist methods.
Frequentists quantify uncertainty also, via confidence sets, and other ways.
Continuous updating has to do with "online learning algorithms," not Bayes.
Bayes is when the target of inference is a posterior distribution. Bonus Bayes points: you don't care about frequentist properties like consistency of the estimator.
Does your argument fail for https://en.wikipedia.org/wiki/Goldbach%27s_weak_conjecture?
If so, can you explain why? If not, it seems your argument is no good, as a good proof of this (weaker) claim exists.
Not that you asked my advice, but I would stay away from number theory unless you get a lot of training.
For the benefit of other readers: this post is confused.
Specifically on this (although possibly also on other stuff): (a) causal and statistical DAGs are fundamentally not the same kind of object, and (b) no practical decision theory used by anyone includes the agent inside the DAG in the way this post describes.
"So if the EDT agent can find a causal structure that reflects their (statistical) beliefs about the world, then they will end up making the same decision as a CDT agent who believes in the same causal structure."
A -> B -> C and A <- B <- C reflect the same statistical beliefs about the world.
If you think it's a hard bet to win, you are saying you agree that nothing bad will happen. So why worry?
Wanna bet some money that nothing bad will come of any of this on the timescales you are worried about?
Some reading on this:
From my experience it pays to learn how to think about causal inference like Pearl (graphs, structural equations), and also how to think about causal inference like Rubin (random variables, missing data). Some insights only arise from a synthesis of those two views.
Pearl is a giant in the field, but it is worth remembering that he's unusual in another way (compared to a typical causal inference researcher) -- he generally doesn't worry about actually analyzing data.
By the way, Gauss figured out not only the normal distribution trying to track down Ceres' orbit, he actually developed the least squares method, too! So arguably the entire loss minimization framework in machine learning came about from thinking about celestial bodies.
Classical RL isn't causal, because there's no confounding (although I think it is very useful to think about classical RL causally, for doing inference more efficiently).
Various extensions of classical RL are causal, of course.
A lot of interesting algorithmic fairness isn't really causal. Classical prediction problems aren't causal.
However, I think domain adaptation, covariate shift, semi-supervised learning are all causal problems.
I think predicting things you have no data on ("what if the AI does something we didn't foresee") is sort of an impossible problem via tools in "data science." You have no data!
It's important to internalize that the intellectual world lives in the attention economy, like eveything else.
Just like "content creators" on social platforms think hard about capturing and keeping attention, so do intellectuals and academics. Clarity and rigor is a part of that.
No one has time, energy, (or crayons, as the saying goes) for half-baked ramblings on a blog or forum somewhere.