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Christian P Robert

Publications and source records attributed to Christian P Robert.

6 recordsLinked to original sources
arXiv2026

Bayesian Adversarial Privacy

Theoretical and applied research into privacy encompasses an incredibly broad swathe of differing approaches, emphases and aims. This work introduces a novel quantitative notion of privacy that is both contextual and specific. Building on and extending ideas from statistical disclosure control and differential privacy, our aim is to model the implications of a disclosure decision in an adversarial setting. Our definition relies on concepts inherent to standard Bayesian decision theory, while departing from them in several important respects. In particular, (i) inference about the data itself becomes meaningful and (ii) the party controlling the release of sensitive information should make disclosure decisions from the prior viewpoint, rather than conditional on the data, which is a feature shared with Bayesian design. Illuminating toy examples are exploited towards highlighting the specificities of the method.

math.ST↗
arXiv2026

Persuasive Privacy

We propose a novel framework for measuring privacy from a Bayesian game-theoretic perspective. This framework enables the creation of new, purpose-driven privacy definitions that are rigorously justified, while also allowing for the assessment of existing privacy guarantees through game theory. We show that pure and probabilistic differential privacy are special cases of our framework, and provide new interpretations of the post-processing inequality in this setting. Further, we demonstrate that privacy guarantees can be established for deterministic algorithms, which are overlooked by current privacy standards.

math.ST↗
arXiv2025

Approximating evidence via bounded harmonic means

Efficient Bayesian model selection relies on the model evidence or marginal likelihood, whose computation often requires evaluating an intractable integral. The harmonic mean estimator (HME) has long been a standard method of approximating the evidence. While computationally simple, the version introduced by Newton and Raftery (1994) potentially suffers from infinite variance. To overcome this issue,Gelfand and Dey (1994) defined a standardized representation of the estimator based on an instrumental function and Robert and Wraith (2009) later proposed to use higher posterior density (HPD) indicators as instrumental functions. Following this approach, a practical method is proposed, based on an elliptical covering of the HPD region with non-overlapping ellipsoids. The resulting estimator, called the Elliptical Covering Marginal Likelihood Estimator (ECMLE), not only eliminates the infinite-variance issue of the original HME and allows exact volume computations, but is also able to be used in multimodal settings. Through several examples, we illustrate that ECMLE outperforms other recent methods such as THAMES and its improved version (Metodiev et al 2024, 2025). Moreover, ECMLE demonstrates lower variance, a key challenge that subsequent HME variants have sought to address, and provides more stable evidence approximations, even in challenging settings.

stat.CO↗
arXiv2024

Sampling using Adaptive Regenerative Processes

Enriching Brownian motion with regenerations from a fixed regeneration distribution $μ$ at a particular regeneration rate $κ$ results in a Markov process that has a target distribution $π$ as its invariant distribution. For the purpose of Monte Carlo inference, implementing such a scheme requires firstly selection of regeneration distribution $μ$, and secondly computation of a specific constant $C$. Both of these tasks can be very difficult in practice for good performance. We introduce a method for adapting the regeneration distribution, by adding point masses to it. This allows the process to be simulated with as few regenerations as possible and obviates the need to find said constant $C$. Moreover, the choice of fixed $μ$ is replaced with the choice of the initial regeneration distribution, which is considerably less difficult. We establish convergence of this resulting self-reinforcing process and explore its effectiveness at sampling from a number of target distributions. The examples show that adapting the regeneration distribution guards against poor choices of fixed regeneration distribution and can reduce the error of Monte Carlo estimates of expectations of interest, especially when $π$ is skewed.

stat.CO↗
arXiv2022

50 shades of Bayesian testing of hypotheses

Hypothesis testing and model choice are quintessential questions for statistical inference and while the Bayesian paradigm seems ideally suited for answering these questions, it faces difficulties of its own ranging from prior modelling to calibration, to numerical implementation. This c

stat.ME↗