Calibration kernel-based ratio estimation for likelihood-free posterior inferenceOA

Bayesian inference often faces challenges where the likelihood function is difficult to evaluate or lacks explicit expression,known as likelihood-free Bayesian problems,where posterior distributions can only be inferred indirectly through samples generated under specific parameters.Existing methods such as approximate Bayesian computation,synthetic likelihood,and Bayesian optimization focus on addressing these issues.This paper extends Miller et al.’s(2022)sequential neural ratio estimation method for likelihood-free Bayesian problems by transforming likelihood-toevidence ratio estimation into a multi-class problem for efficient posterior estimation.We introduce a new calibration kernel-based ratio estimation method(CKRE),to enhance the original method’s training efficiency and performance.The convergence of our proposed method is proven,and numerical experiments demonstrate its significant improvement in accurately estimating posterior distributions under limited sample generation conditions.