An efficient Monte Carlo method for valid prior-free possibilistic statistical inference
本文针对无先验的推断模型（IM）在计算上的挑战，提出一种新的蒙特卡罗方法，通过近似IM的可能性输出，实现高效且准确的统计推断。
Inferential models (IMs) offer prior-free, Bayesian-like posterior degrees of belief designed for statistical inference, which feature a frequentist-like calibration property that ensures reliability of said inferences. The catch is that IMs’ degrees of belief are possibilistic rather than probabilistic and, since the familiar Monte Carlo methods approximate probabilistic quantities, there are significant computational challenges associated with putting this framework into practice. The present paper overcomes these challenges by developing a new Monte Carlo method designed specifically to approximate the IM’s possibilistic output. The proposal is based on a characterization of the possibilistic IM’s credal set, which identifies the “best probabilistic approximation” of the IM as a mixture distribution that can be readily approximated and sampled from. These samples can then be transformed into an approximation of the possibilistic IM. Numerical results are presented highlighting the proposed approximation’s accuracy and computational efficiency.