Besov priors are nonparametric priors that model spatially inhomogeneous functions. They are routinely used in inverse problems and imaging, where they exhibit attractive sparsity-promoting and edge-preserving features. A recent line of work has initiated the study of the asymptotic frequentist convergence properties of Besov priors. In the present paper, we consider the theoretical recovery performance of the associated posterior distributions in the density estimation model, under the assumption that the observations are generated by a spatially inhomogeneous true density belonging to a Besov space. We improve on existing results and show that carefully tuned Besov priors attain optimal posterior contraction rates. Furthermore, we show that a hierarchical procedure involving a hyper-prior on the regularity parameter leads to adaptation to any smoothness level.

翻译：贝索夫前列物是模拟空间不相容功能的非参数前列物,通常用于反向问题和成像,展示有吸引力的聚度促进和边缘保护特征。最近的一项工作开始研究贝索夫前列物的无症状常态趋同特性。在本文件中,我们考虑了密度估计模型中相关后端分布的理论恢复性能,假设观测结果来自属于贝索夫空间的空间不相容真实密度。我们改进了现有结果,并表明仔细调整的贝索夫前列物达到最佳后端收缩率。此外,我们表明,一个涉及常态参数超优先性的等级程序导致对平稳水平的适应。