Deep Fiducial Inference

TL;DR

This paper introduces a novel autoencoder-based method for computing generalized fiducial distributions, offering an alternative to MCMC, with improved accuracy and coverage in complex statistical inference problems.

Contribution

It proposes a fiducial autoencoder (FAE) and an approximate fiducial computation (AFC) algorithm to efficiently generate and refine fiducial samples, enhancing inference in complex models.

Findings

FAE effectively generates fiducial samples.

AFC improves the accuracy of fiducial inference.

Method shows excellent coverage in numerical experiments.

Abstract

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), we design a fiducial autoencoder (FAE). The fitted autoencoder 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.