I hadn’t actually heard of Laplace’s approximation—definitely relevant! The catch about the dimension is a good one.
In the large causal model, is the issue just that
there is one multiplication per variable
some dependence chains don’t have very many variables in them
in those few-variable chains, we might not get enough multiplications to converge?
If that is the issue, weird nasty operations occur to me, like breaking variables up into sub and sub-sub variables, to get more multiplications, which might get more Gaussian. (For example, splitting the node “Maxwell finishes writing this comment” into “his computer doesn’t run out of battery” and “the police don’t suddenly bust into his apartment”). Whether or not it’s worth doing, I wonder—would this actually work to make things more Gaussian? Or is there some… conservation of convergence… that makes it so you can’t get closer to Gaussian by splitting variables up? [Don’t feel like you have to answer these—they’re more just me following up on thoughts I got from your comment].
Thank you!
I hadn’t actually heard of Laplace’s approximation—definitely relevant! The catch about the dimension is a good one.
In the large causal model, is the issue just that
there is one multiplication per variable
some dependence chains don’t have very many variables in them
in those few-variable chains, we might not get enough multiplications to converge?
If that is the issue, weird nasty operations occur to me, like breaking variables up into sub and sub-sub variables, to get more multiplications, which might get more Gaussian. (For example, splitting the node “Maxwell finishes writing this comment” into “his computer doesn’t run out of battery” and “the police don’t suddenly bust into his apartment”). Whether or not it’s worth doing, I wonder—would this actually work to make things more Gaussian? Or is there some… conservation of convergence… that makes it so you can’t get closer to Gaussian by splitting variables up? [Don’t feel like you have to answer these—they’re more just me following up on thoughts I got from your comment].
I accept your affordance, and thank you, this will make me more likely to comment on your posts in the future.