A0350
Title: Insufficient Gibbs sampling
Authors: Christian Robert - Universite Paris-Dauphine (France) [presenting]
Robin Ryder - Imperial College London (United Kingdom)
Antoine Luciano - Universite Paris Dauphine PSL (France)
Abstract: In some applied scenarios, the availability of complete data is restricted, often due to privacy concerns; only aggregated, robust and inefficient statistics derived from the data are made accessible. These robust statistics are not sufficient, but they demonstrate reduced sensitivity to outliers and offer enhanced data protection due to their higher breakdown point. A parametric framework is considered, and a method to sample from the posterior distribution of parameters conditioned on various robust and inefficient statistics is proposed: specifically, the pairs (median, MAD) or (median, IQR), or a collection of quantiles. The approach leverages a Gibbs sampler and simulates latent augmented data, which facilitates simulation from the posterior distribution of parameters belonging to specific families of distributions. A by-product of these samples from the joint posterior distribution of parameters and data given the observed statistics is that it can estimate Bayes factors based on observed statistics via bridge sampling. The limitations of the proposed methods are validated and outlined through toy examples and an application to real-world income data.
