Rates of convergence for Gibbs sampling in the analysis of almost exchangeable data

10/29/2020

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by   Balázs Gerencsér, et al.

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Motivated by de Finetti's representation theorem for partially exchangeable arrays, we want to sample 𝐩∈ [0,1]^d from a distribution with density proportional to (-A^2∑_i<jc_ij(p_i-p_j)^2). We are particularly interested in the case of an almost exchangeable array (A large). 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 Θ(A^2) steps in a suitable Wasserstein distance. The upper and lower bounds are explicit and depend on the matrix C through few relevant spectral parameters.