I think the motivation for the representability of some sets of conditional independences with a DAG is pretty clear, because people already use probability distributions all the time, they sometimes have conditional independences and visuals are nice.
On the other hand the fundamental theorem relates orthogonality to independences in a family of distributions generated in a particular way. Neither of these things are natural properties of probability distributions in the way that conditional independence is. If I am using probability distributions, it seem...
I don't understand the motivation behind the fundamental theorem, and I'm wondering if you could say a bit more about it. In particular, it suggests that if I want to propose a family of probability distributions that "represent" observations somehow ("represents" maybe means in the sense of Bayesian predictions or in the sense of frequentist limits), I want to also consider this family to arise from some underlying mutually independent family along with some function. I'm not sure why I would want to propose an underlying family and a function at all, and...
Hmm, I am not sure what to say about the fundamental theorem, because I am not really understanding the confusion. Is there something less motivating about the fundamental theorem, than the analogous theorem about d-seperation being equivalent to conditional independence in all distributions comparable with the DAG?
Maybe this helps? (probably not): I am mostly imagining interacting with only a single distributions in the class, and the claim about independence in all probability distributions comparable with the structure can be replaced with instead indep...
Sounds awful to me. I would absolutely hate to live somewhere where I was regularly told what to do and/or expected to fit in with rituals. I tolerate this kind of thing at work because I have to.
What will you say when people come to you saying "I'm not sure this is really worth it for me"? I personally don't think self-improvement is a very stable overall goal. In my cursory acquaintance, most cults/high-demand living situations tend to believe in "something greater" - often something quite ridiculous, but nonetheless something bigger than the individual. Perhaps it is important to have something which seems to trump feelings of personal discomfort.
Speaking personally, I think something like #1 is true on the grounds that I have seen many cases of white Australian people, often with considerable power, acting in excessively patronising and authoritarian ways towards Aboriginal people and I have no difficulty believing that similar things happen in the US.
However, I also do not think that racial disparities in outcomes are almost all caused by #1; in fact I think that probably less than 50% of almost any particular disparity is caused by #1. Thus, I think that outcome disparities are at best weak evid... (read more)