Moritz Schauer

@mschauer.bsky.social

Statistician, Associate Professor (Lektor) at University of Gothenburg and Chalmers; inference and conditional distributions for anything https://mschauer.github.io http://orcid.org/0000-0003-3310-7915 [ˈmoː/r/ɪts ˈʃaʊ̯ɐ]

Probability theory causes a certain mathematical inflation: random variables are functions, events are sets, and probabilities are countably additive set functions of total mass one defined on σ-algebras.

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

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

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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).

The event B having happened is not the same as the receiving the information O that the event B has happened, because you also condition on receiving the information at all in the latter case. Conflating this contributes a lot to the "paradoxa" such as boy/girl paradox, Monty Hall...

For the applicability of Bayes' theorem, it is important when the information $B$ you condition on is actually available.

Let $O \subset B$ be the event of observing $B$ with $P(O)>0$. If $O$ and $A$ are independent with respect to $P_{|B}(\cdot) = P(\cdot \mid B)$, 
then 
\[
P(A\mid O) = P(A \mid B).
\]

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AITHYRA Research Institute of the Austrian Academy of Sciences@aithyra.bsky.social · 10mo ago

The Starting Principal Investigators at #AITHYRA the Research Institute for Biomedical Artificial Intelligence of the OeAW in Vienna invite outstanding candidates to apply for postdoctoral positions in the field of AI/ML & Life Sciences. www.oeaw.ac.at/aithyra/post... Please apply by 20 Nov 2025!

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