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Title: Deep fiducial inference Authors:  Gang Li - University of Washington at Seattle (United States) [presenting]
Jan Hannig - University of North Carolina at Chapel Hill (United States)
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). An alternative way of computing a generalized fiducial distribution is proposed that could be used in complex situations. In particular, to overcome the difficulty when the unnormalized fiducial density (needed for MCMC) is intractable, a fiducial autoencoder (FAE) is designed. The fitted FAE is used to generate generalized fiducial samples of the unknown parameters. To increase accuracy, an approximate fiducial computation (AFC) algorithm is then applied, by rejecting samples that when plugged into a decoder do not replicate the observed data well enough. The numerical experiments show the effectiveness of the FAE-based inverse solution and the excellent coverage performance of the AFC-corrected FAE solution.