Pokie: Posterior Accuracy and Model Comparison

We present Pokie, a sample-based method for comparing posterior distributions. Pokie estimates the expected probability that samples from an inferred posterior match the true, unknown posterior of a probabilistic model for which only joint samples are available. This framework enables direct Bayesian model comparison by assessing how each model's posterior distribution aligns with the posterior of the true model, all while avoiding evidence computation and relying solely on simulations. We show that Pokie converges to a score of $2/3$ under well-specified models and has a lower bound of $1/2$ in the worst case. We demonstrate its effectiveness across several toy problems and cosmological inference tasks.