Our local Mostly (and monthly) Monte Carlo seminar is back for a new academic year, now organized by Antoine Luciano and Timothy Johnston. The first session will take place at the PariSanté Campus on Friday 17 October 2025 (3:00pm, room 07), with the organisers opening the dance, with two talks:
3pm Timothy Johnston (CEREMADE, Université Paris Dauphine–PSL): Differential Privacy of Markov Chains
Joint work with Andrea Bertazzi, Alain Durmus and Gareth Roberts
In this talk we shall discuss differential privacy, a framework for quantifying the extent to which a random output depends on the information used to produce it. After introducing several related definition of differential privacy, we shall discuss techniques used to show the differential privacy of both trajectories and single draws from Markov Chains. In doing so we shall touch on a perturbation technique which allows for Wasserstein type bounds to be converted into stronger distances like the KL and Renyi divergence.
4pm Antoine Luciano (CEREMADE, Université Paris Dauphine–PSL): Permutations accelerate Approximate Bayesian Computation
Joint work with Charly Andral, Christian P. Robert and Robin J. Ryder
Approximate Bayesian Computation (ABC) methods have become essential tools for performing inference when likelihood functions are intractable or computationally prohibitive. However, their scalability remains a major challenge in hierarchical or high-dimensional models. In this paper, we introduce permABC, a new ABC framework designed for settings with both global and local parameters, where observations are grouped into exchangeable compartments. Building upon the Sequential Monte Carlo ABC (ABC-SMC) framework, permABC exploits the exchangeability of compartments through permutation-based matching, significantly improving computational efficiency. We then develop two further, complementary sequential strategies: Over Sampling, which facilitates early-stage acceptance by temporarily increasing the number of simulated compartments, and Under Matching, which relaxes the acceptance condition by matching only subsets of the data. These techniques allow for robust and scalable inference even in high-dimensional regimes. Through synthetic and real-world experiments – including a hierarchical Susceptible-Infectious-Recover model of the early COVID-19 epidemic across 94 French departments – we demonstrate the practical gains in accuracy and efficiency achieved by our approach.
