Since the mid‐2000s, there has been a resurrection of interest in modern modifications of fiducial inference. To date, the main computational tool to extract a generalized fiducial distribution is Markov chain Monte Carlo (MCMC). We propose an alternative way of computing a generalized fiducial distribution that could be used in complex situations. In particular, to overcome the difficulty when the unnormalized fiducial density (needed for MCMC) is intractable, we design a fiducial autoencoder (FAE). The fitted FAE is used to generate generalized fiducial samples of the unknown parameters. To increase accuracy, we then apply an approximate fiducial computation (AFC) algorithm, by rejecting samples that when plugged into a decoder do not replicate the observed data well enough. Our numerical experiments show the effectiveness of our FAE‐based inverse solution and the excellent coverage performance of the AFC‐corrected FAE solution.

中文翻译：

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深入的基准推理

自2000年代中期以来，对基准推理的现代修改引起了人们的兴趣。迄今为止，提取广义基准分布的主要计算工具是马尔可夫链蒙特卡洛（MCMC）。我们提出了一种计算广义基准分布的替代方法，该方法可以在复杂情况下使用。特别地，为了克服难以标准化的基准密度（MCMC所需）难以解决的困难，我们设计了基准自动编码器（FAE）。拟合的FAE用于生成未知参数的广义基准样本。为了提高准确性，我们然后通过拒绝样本（当插入解码器时无法很好地复制观察到的数据）来应用近似基准计算（AFC）算法。