Abstract
In this paper, under the Dobrushin’s uniqueness condition, we obtain explicit estimates of the geometrical convergence rate for the random scan Gibbs sampler in the Wasserstein metric.
Highlights
Let μ be a Gibbs probability measure on EN with dimension N, i.e., μ(dx1, · · ·, dxN ) =EN e−V e−V (x1,···,xN ) (x1,···,xN )π(dx1) · ·· π(dx1) π(dxN )· · π(dxN ), where π is some σ-finite reference measure on E
E−V (x1,···,xN ) e−V (x1,···,xN )π(dxi) π(dxi), which is a one-dimensional measure, easy to simulate in practice
The scheme of the random scan Gibbs sampler approximating μ is that, in each iteration, one randomly chooses one coordinate to update according to the one-dimensional conditional distributions μi, i = 1, · · ·, N
Summary
In order to approximate μ via iterations of the one-dimensional conditional distributions μi, i = 1, · · · , N, the various scan Gibbs samplers are often used (see [4]). In [6], Wu and the author studied systematic scan Gibbs sampler by Dobrushin’s uniqueness conditions. The scheme of the random scan Gibbs sampler approximating μ is that, in each iteration, one randomly chooses one coordinate to update according to the one-dimensional conditional distributions μi, i = 1, · · · , N.
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