Deep fiducial inference
Deep fiducial inference
复制标题
深度基准推理
作者：
Li, Gang;Hannig, Jan
自 2000 年代中期以来，人们对基准推理的现代修改产生了兴趣。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罗（MCMC）。我们提出了一种计算可在复杂情况下使用的广义基准分布的替代方法。特别是，为了克服非标准化基准密度（MCMC 所需）难以处理的困难，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，我们然后应用近似基准计算（AFC）算法，通过拒绝插入解码器时不能很好地复制观察到的数据的样本。我们的数值实验表明了基于 FAE 的逆解的有效性以及 AFC 校正的 FAE 解的出色覆盖性能。
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.