I just updated my preprint (https://arxiv.org/abs/1804.07833) on arXiv after major revisions following reviewer comments. Here’s the new abstract:
We introduce two classes of Metropolis-Hastings algorithms for sampling target measures that are absolutely continuous with respect to underlying non-Gaussian measures on infinite-dimensional Hilbert spaces. We particularly focus on measures that are highly non-Gaussian and utilize certain properties of the underlying prior measures to construct autoregressive-type proposal kernels that are prior reversible and result in algorithms that satisfy detailed balance with respect to the target measures. We then introduce a new class of prior measures, called the Bessel-K priors, as a generalization of the gamma distribution to measures in infinite dimensions. The Bessel-K priors interpolate between well-known priors such as the gamma distribution and Besov priors and can model sparse or compressible parameters. We present concrete instances of our algorithms for the Bessel-K priors and present numerical examples in density estimation, finite-dimensional denoising and deconvolution on the circle.