Convergence and perturbation theory for an infinite-dimensional Metropolis-Hastings algorithm with self-decomposable priors
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We study a Metropolis-Hastings algorithm for target measures that are absolutely continuous with respect to a large class of 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 Cesáro averages and other pathwise quantities. 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 via perturbation theory.
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