论文标题
使用$ p $ - 指示先验的白噪声模型中的BESOV空间的自适应推断
Adaptive inference over Besov spaces in the white noise model using $p$-exponential priors
论文作者
论文摘要
在许多科学应用中，目的是推断出在某些领域平稳但在其领域其他领域的粗糙甚至不连续的功能。这种空间不均匀函数可以在具有合适的集成性参数的BESOV空间中进行建模。在这项工作中，我们使用$ p $ - 指数的先验研究了在白噪声模型中对BESOV空间进行自适应贝叶斯的推论，在白噪声模型中，$ p $ - 指数的先验范围介于拉普拉斯和高斯之间，并且具有规律性和扩展超参数。为了实现适应，我们采用经验和分层贝叶斯方法来调整这些超参数。我们的结果表明，尽管众所周知，高斯先验只能在空间均匀函数的空间中达到最小速率，但拉普拉斯先生的先验达到了最小值或几乎在空间均匀函数的BESOV空间中的最小值和最小速率，并且BESOV空间允许空间不固定性。
In many scientific applications the aim is to infer a function which is smooth in some areas, but rough or even discontinuous in other areas of its domain. Such spatially inhomogeneous functions can be modelled in Besov spaces with suitable integrability parameters. In this work we study adaptive Bayesian inference over Besov spaces, in the white noise model from the point of view of rates of contraction, using $p$-exponential priors, which range between Laplace and Gaussian and possess regularity and scaling hyper-parameters. To achieve adaptation, we employ empirical and hierarchical Bayes approaches for tuning these hyper-parameters. Our results show that, while it is known that Gaussian priors can attain the minimax rate only in Besov spaces of spatially homogeneous functions, Laplace priors attain the minimax or nearly the minimax rate in both Besov spaces of spatially homogeneous functions and Besov spaces permitting spatial inhomogeneities.
