I’m still struggling to understand hypothesis testing . . . leading to a more general discussion of the role of assumptions in statistics

I’m sitting at this talk where Thomas Richardson is talking about testing the hypothesis regarding a joint distribution of three variables, X1, X2, X3. The hypothesis being tested is that X1 and X2 are conditionally independent given X3. I don’t have a copy of Richardson’s slides, but here’s a paper that I think it related, …