论文标题
Gibbs抽样的收敛速率在分析几乎可交换数据中
Rates of convergence for Gibbs sampling in the analysis of almost exchangeable data
论文作者
论文摘要
由de Finetti的表示定理的动机几乎可以交换的阵列，我们想在[0,1]^d $中采样$ \ mathbf p \ in [0,1]^d $，其密度与$ \ exp（-a^2 \ sum_ {i <j} c_} c_} c_ {ij} c_ {ij}（iji-p_j）（p_i-p_j）（p_i-p_j）$，非负重。我们分析了用于模拟这些度量的坐标Gibbs采样器的收敛速率。我们表明，对于每个非零固定矩阵$ c =（c_ {ij}）$，并且大量$ a $，混合发生在$θ（a^2）$ steps $ sept以合适的Wasserstein距离中。上限和下限是显式的，并且通过少数相关的光谱参数取决于矩阵$ c $。
Motivated by de Finetti's representation theorem for almost exchangeable arrays, 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 non-zero 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.
