August 2024 Adaptive inference over Besov spaces in the white noise model using p-exponential priors
Sergios Agapiou, Aimilia Savva
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Bernoulli 30(3): 2275-2300 (August 2024). DOI: 10.3150/23-BEJ1673


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 lead to adaptive or nearly adaptive procedures in both Besov spaces of spatially homogeneous functions and Besov spaces permitting spatial inhomogeneities.


The authors are deeply grateful to Botond Szabo for numerous explanations and many useful discussions regarding the general theory of [36]. The authors are also grateful to Omiros Papaspiliopoulos for useful guidance regarding the implementation of the studied procedures. Finally, the authors thank two anonymous referees, the AE and the editor for many helpful comments.


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Sergios Agapiou. Aimilia Savva. "Adaptive inference over Besov spaces in the white noise model using p-exponential priors." Bernoulli 30 (3) 2275 - 2300, August 2024.


Received: 1 September 2022; Published: August 2024
First available in Project Euclid: 14 May 2024

Digital Object Identifier: 10.3150/23-BEJ1673

Keywords: Adaptation , Besov spaces , Empirical Bayes , Gaussian prior , hierarchical Bayes , Laplace prior , Posterior contraction rates , spatially inhomogeneous functions , White noise model


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Vol.30 • No. 3 • August 2024
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