I know that ABC is commonly used when the likelihood is intractable, so likelihood principle is not an interest in that case. But, I am curious whether the ABC satisfies the likelihood principle when the likelihood function is tractable. ABC is a generative procedure to sample parameters from posterior, and likelihood principle says that the inference on the parameter should be solely determined by likelihood part ignoring the term of the observation.
I think that if I generate fake samples from a parameter, the generating process is crucially affected by the term of observation, which might be ignored in the likelihood principle.
It's confusing, because I think that the ABC does not follow the likelihood principle, but it is well-known that Bayesian stat follows it.
Am I missing something?