Yes, that's the contrast of interest
The relevant observations are imo 1. MH is a causal inference problem first and a probability problem second, and 2. the association usually called collider bias is information you can make use of for decision rather than just being, as it normally is, a problem
I have not getting filter coffee in a coffee place and not getting gyros in a Greek restaurant until acing the local speech patterns… Don’t people have priors?? PS: ”Chyros? really, Dutch friends, chyros?”
Dust behaves as if someone put a minus sign in front of the Laplacian: dust ends up in the corners instead of spread out.
The key to a successful career is dying wealthy
Witnessing the birth of the marginal differential product theory about hiring your enemies
I like that people genuine think in intervals. Maybe there is hope to explain the confidence interval
This is basically my villain origin story.
"How old are you?" (unique responses)
My slides are of course not a text book, but I link them here because they are opinionated that perhaps you can get away without GES or PC and get there by compute and a simpler hill climbing algorithm maximising the likelihood/ searching a MAP github.com/mschauer/Cau...
For me for a song to click there must be specific harmonic patterns present, you have them in m.youtube.com/watch?v=EKe9... for example but also in the notorious C&A song m.youtube.com/watch?v=UFDn...
Well, me probably before figuring it out, lol
And some point I had to notice how many songs I like are David Bowie covers and I suspect David Bowie is too genius for me. This one for example, I can understand it through Nirvana, which are probably also geniuses though www.youtube.com/watch?v=freg...,
3.4m² ? I wouldn’t have painted the underside
It’s not only easy to spot. It’s hard to unsee.
p=0.048, but in an enlightened way
If your niche is small enough, every post is a viral post.
wikipedia turns 25 today! the last unenshittified major website! backbone of online info! triumph of humanity! powered by urge of unpaid randos to correct each other! somehow mostly reliable! "good thing wikipedia works in practice, because it sure doesn't work in theory" - old wiki adage
Yeah, the Kalman gain K is the regression coefficient, so the conditional mean is old mean plus observations scaled by K. If you write K (H Σ⁻ Hᵀ + Σ_ε) = Σ⁻ Hᵀ you see how it is aligned with the normal equations A Σ₂₂ = Σ₁₂ from above.
In general, residuals of linear regression are only uncorrelated with the predictors, not independent, so their conditional mean need not vanish. Gaussianity upgrades uncorrelatedness to independence; once this happens, the linear predictor becomes the mean of the conditional distribution.
Have a look here: stats.stackexchange.com/a/30600
The trick: choose A by the normal equation A Σ₂₂ = Σ₁₂ and see that X₁ − A X₂ is uncorrelated with X₂, and by Gaussianity also independent. So E[X₁∣X₂] = A X₂. Even works in the singular case.
At a technical university the steps of Pearl’s ladder are called stochastics, stochastic control and optimal transport
Yeah, more oil and less integrals
Mostly echoing your statement bsky.app/profile/p-hu... The do-operator formalizes how a system acts to interventions, so certain statements about interventions become propositions in a calculus, but you still have to argue how this maps to the system you want to describe.
Pearl is maybe also dismissive of this meta level, whereas people do make clean meta-level arguments for RCTs etc, in fact it is unavoidable, cf @p-hunermund.com
In classical approaches, correctness of causal claims is argued at the meta level, by appealing to design or understanding. In the do-calculus, that burden is shifted into a mathematical formalism.
Causal inference is often hidden in plain sight. In a randomized clinical trial, the setup is such that interventional and conditional distributions coincide.
That is E(X | do(T = t)) = E(X | T = t).
Love it. Adding Sid Meier's Beta Centauri
(and point null is the worst case for an error in the directional statements)
By the way, I am quite okay with users drawing directional conclusions after rejecting a two-sided null hypothesis; because the error rate under the point null is the same as that of the original test.