论文标题
密度估算中的BESOV-LAPLACE先验：最佳后收缩率和适应性
Besov-Laplace priors in density estimation: optimal posterior contraction rates and adaptation
论文作者
论文摘要
BESOV先验是非参数先验，可以在空间上模拟不均匀的功能。它们通常在反问题和成像中使用，在这些问题和成像中，它们表现出诱人的稀疏性和边缘性功能。最近的一项工作已经开始研究其渐近频率融合特性。在本文中，我们考虑了在密度估计模型中与BESOV-LAPLACE先验相关的后验分布的理论恢复性能，假设观测值是由可能在空间上属于BESOV空间的空间不均匀的真实密度产生的。我们改善了现有结果，并表明精心调整的BESOV-LAPLACE先验达到了最佳的后部收缩率。此外，我们表明涉及规律性参数超级优先级的分层过程导致适应任何平滑度。
Besov priors are nonparametric priors that can 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 their asymptotic frequentist convergence properties. In the present paper, we consider the theoretical recovery performance of the posterior distributions associated to Besov-Laplace priors in the density estimation model, under the assumption that the observations are generated by a possibly spatially inhomogeneous true density belonging to a Besov space. We improve on existing results and show that carefully tuned Besov-Laplace priors attain optimal posterior contraction rates. Furthermore, we show that hierarchical procedures involving a hyper-prior on the regularity parameter lead to adaptation to any smoothness level.
