arXiv subjects

Cameron Bell

Publications and source records attributed to Cameron Bell.

3 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↗

arXiv2024

Adaptive Stereographic MCMC

In order to tackle the problem of sampling from heavy tailed, high dimensional distributions via Markov Chain Monte Carlo (MCMC) methods, Yang, Latuszy\'nski, and Roberts (2022) (arXiv:2205.12112) introduces the stereographic projection as a tool to compactify $\mathbb{R}^d$ and transform the problem into sampling from a density on the unit sphere $\mathbb{S}^d$. However, the improvement in algorithmic efficiency, as well as the computational cost of the implementation, are still significantly impacted by the parameters used in this transformation. To address this, we introduce adaptive versions three stereographic MCMC algorithms - the Stereographic Random Walk (SRW), the Stereographic Slice Sampler (SSS), and the Stereographic Bouncy Particle Sampler (SBPS) - which automatically update the parameters of the algorithms as the run progresses. The adaptive setup allows to better exploit the power of the stereographic projection, even when the target distribution is neither centered nor homogeneous. Unlike Hamiltonian Monte Carlo (HMC) and other off-the-shelf MCMC samplers, the resulting algorithms are robust to starting far from the mean in heavy-tailed, high-dimensional settings. To prove convergence properties, we develop a novel framework for the analysis of adaptive MCMC algorithms over collections of simultaneously uniformly ergodic Markov operators, which is applicable to continuous-time processes, such as SBPS. This framework allows us to obtain $\mathcal{L}^2$ and almost sure convergence results, and a CLT for our adaptive stereographic algorithms.

stat.CO↗

arXiv2020

Discovering Exotic AGN behind the Magellanic Clouds

The nearby Magellanic Clouds system covers more than 200 square degrees on the sky. Much of it has been mapped across the electromagnetic spectrum at high angular resolution and sensitivity X-ray (XMM-Newton), UV (UVIT), optical (SMASH), IR (VISTA, WISE, Spitzer, Herschel), radio (ATCA, ASKAP, MeerKAT). This provides us with an excellent dataset to explore the galaxy populations behind the stellar-rich Magellanic Clouds. We seek to identify and characterise AGN via machine learning algorithms on this exquisite data set. Our project focuses not on establishing sequences and distributions of common types of galaxies and active galactic nuclei (AGN), but seeks to identify extreme examples, building on the recent accidental discoveries of unique AGN behind the Magellanic Clouds.

astro-ph.GA↗