That would be pretty reasonable, but it would make the model comparison part even harder. I do need P[X] (and therefore Z) for model comparison; this is the challenge which always comes up for Bayesian model comparison.
Why does it make Bayesian model comparison harder? Wouldn’t you get explicit predicted probabilities for the data X from any two models you train this way? I guess you do need to sample from the Gaussian in λ a few times for each X and pass the result through the flow models, but that shouldn’t be too expensive.
That would be pretty reasonable, but it would make the model comparison part even harder. I do need P[X] (and therefore Z) for model comparison; this is the challenge which always comes up for Bayesian model comparison.
Why does it make Bayesian model comparison harder? Wouldn’t you get explicit predicted probabilities for the data X from any two models you train this way? I guess you do need to sample from the Gaussian in λ a few times for each X and pass the result through the flow models, but that shouldn’t be too expensive.