I am reading the normalizing flows review article by Deepmind and came across a sentence that I don't understand in section 6.2.4 Likelihood-Free Inference regarding use of normalizing flows to supplement likelihood-free inference.
I'm familiar that likelihood-free inference is a form of Approximate Bayesian Computation (ABC), where simulated data, $x$, from a model with parameters $\eta$, is used to approximate the posterior $p(\eta|x)$ or intractable likelihood, $p(x|\eta)$. However, one sentence in the last paragraph of the section trips me up: "Assuming a tractable prior distribution $p(\eta)$ over the parameters of interest..."
What does it mean to have a tractable prior distribution $p(\eta)$ for a simulator-based model?
I'm assuming this translates to "the prior for the parameter of interest should be reasonable for the problem at hand." For example, if we're using this for a high-energy physics model (cited in Deepmind paper), then the prior for the parameter is tractable if it's flat and within the range of reasonable parameter values and intractable if it's, for example, flat and doesn't include the most likely parameter value in its domain.
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