/blog/2021/12/20/fully-bayesian-ate-iptw/

[andrewheiss]

How to create a(n almost) fully Bayesian outcome model with inverse probability weights | Andrew Heiss
https://www.andrewheiss.com/blog/2021/12/20/fully-bayesian-ate-iptw/

[andrewheiss]

Originally posted by Jonas Esser on 2022-01-06 16:24:21

Interesting! I am a PhD student in Amsterdam and have had ideas along
similar lines. But I don't think I'm satisfied with this approach. As
far as I understand, this is not a fully Bayesian method and does not
give you a valid posterior.

You first obtain samples of propensity scores and then feed them to the
outcome model as if they were observed data. But they're not, they are
parameters. You create an artificial separation between the parameters
in the treatment model and the outcome model, forcing independence
which, according to your own model specification, does not hold. In a
fully Bayesian analysis all parameters must be estimated jointly; this
is exactly the point that Robins makes in his articles.

I could be wrong though, happy to discuss.

[andrewheiss]

Originally posted by Jonas on 2022-01-06 16:29:23

To clarify: either outcome and propensity score are independent, in
which case you cannot use the propensity score to predict the outcome,
or they are dependent, in which case they have to be estimated jointly.
You cannot have it both ways.