Spectral gaps and error estimates for infinite-dimensional Metropolis–Hastings with non-Gaussian priors
Spectral gaps and error estimates for infinite-dimensional Metropolis–Hastings with non-Gaussian priors
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DOI：
10.1214/22-aap1854
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发表时间：
2018-09
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通讯作者：
Bamdad Hosseini;J. Johndrow
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文献类型：
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作者：
Bamdad Hosseini;J. Johndrow
我们研究了目标度量的一类大都市杂货算法，这些算法与大型的Banach空间上的非高斯事先措施绝对连续。该算法显示在通过Lyapunov函数加权的类似于Wasserstein的半明细性中具有光谱差距。为算法的计算处理近似值提供了许多误差边界，包括通过扰动理论的CES \'{a} RO平均值和其他路径数量的接近度的界限。几种应用说明了结果应用的问题，例如盖勒金型预测的离散化和提案的近似模拟。
We study a class of Metropolis-Hastings algorithms for target measures that are absolutely continuous with respect to a large class of non-Gaussian prior measures on Banach spaces. The algorithm is shown to have a spectral gap in a Wasserstein-like semimetric weighted by a Lyapunov function. A number of error bounds are given for computationally tractable approximations of the algorithm including bounds on the closeness of Ces\'{a}ro averages and other pathwise quantities via perturbation theory. Several applications illustrate the breadth of problems to which the results apply such as discretization by Galerkin-type projections and approximate simulation of the proposal.