Gerencsér Balázs (Rényi Intézet és ELTE): Convergence analysis of Gibbs sampler motivated by almost exchangeable data

Motivated by the first steps of working with almost exchangeable data in a Bayesien setting, de Finetti's representation theorem for almost exchangeable arrays is at the core.
In relation with the prior distribution, we want to sample $\mathbf p \in [0,1]^d$ from a distribution with density proportional to $\exp(-A^2 \sum_{i < j} c_{ij} (p_i-p_j)^2)$, where $A$ is large and $c_{ij}$'s are non-negative weights.
We analyze the rate of convergence of a coordinate Gibbs sampler used to simulate from these measures. We show that for every fixed matrix $C=(c_{ij})$, and large enough $A$, mixing happens in $\Theta_C(A^2)$ steps in a suitable Wasserstein distance.
Joint work with Andrea Ottolini.