All of AidanGoth's Comments + Replies

I thought it dealt with these ok -- could you be more specific?

It's linear because it's an expectation. It is under-specified in that it needs us to assume or prove the marginal distributions for the $X_i$ and I guess that's problematic if an algorithm for doing that is a big part of what the authors are looking for. But if we do have marginal distributions for each $X_i$, then $E\left(X_i^2\right),E\left(X_i^{\prime 2}\right),E\left(X_i^{\prime 2}|{\pi }^{\prime }\right)$ are well-defined and $\tilde{E}\left({\sum }_{i=1}^n{X}_i^2|\pi \right)={\sum }_{i=1}^{n}E\left(X_i^{\prime 2}|{\pi }^{\prime }\right)$.

This question is in the spirit of "I think I'm doing something dumb / obviously wrong -- help me see why" but it's maybe too niche for this thread. (Answers that redirect me to a better place to ask are welcome.)

I recently read Paul Christiano, Eric Neyman and Mark Xu's "Formalizing the presumption of independence" (https://arxiv.org/pdf/2211.06738.pdf). My understanding is that they aim to formalise some types of reasonable (but defeasible) “hand-waving” in otherwise formal proofs, in a way that maintains the underlying deductive structure of a formal pro... (read more)