87 citations · 184 across the 14 of their papers we have counts for
12 papers · 1 filter
Leveraging tails for adaptation
Sergios Agapiou, Ismaël Castillo, Paul Egels
We consider contraction of Bayesian posterior distributions in nonparametric settings where coefficients of a function over a basis or dictionary are given priors with --exponen…
Heavy-tailed and Horseshoe priors for regression and sparse Besov rates
Sergios Agapiou, Ismaël Castillo, Paul Egels
The large variety of functions encountered in nonparametric statistics, calls for methods that are flexible enough to achieve optimal or near-optimal performance over a wide variet…
Heavy-tailed Bayesian nonparametric adaptation
Sergios Agapiou, Ismaël Castillo
We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy tailed series priors. We illustrate it in a variety of settings, showing in p…
Adaptive inference over Besov spaces in the white noise model using -exponential priors
Sergios Agapiou, Aimilia Savva
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 inhomogen…
Laplace priors and spatial inhomogeneity in Bayesian inverse problems
Sergios Agapiou, Sven Wang
Spatially inhomogeneous functions, which may be smooth in some regions and rough in other regions, are modelled naturally in a Bayesian manner using so-called Besov priors which ar…
Designing truncated priors for direct and inverse Bayesian problems
Sergios Agapiou, Peter Mathé
The Bayesian approach to inverse problems with functional unknowns, has received significant attention in recent years. An important component of the developing theory is the study…
Rates of contraction of posterior distributions based on -exponential priors
Sergios Agapiou, Masoumeh Dashti, Tapio Helin
We consider a family of infinite dimensional product measures with tails between Gaussian and exponential, which we call -exponential measures. We study their measure-theoretic…
Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems
Sergios Agapiou, Martin Burger, Masoumeh Dashti +1
We consider the inverse problem of recovering an unknown functional parameter in a separable Banach space, from a noisy observation of its image through a known possibly no…
Preconditioning the prior to overcome saturation in Bayesian inverse problems
Sergios Agapiou, Peter Mathé
We study Bayesian inference in statistical linear inverse problems with Gaussian noise and priors in Hilbert space. We focus our interest on the posterior contraction rate in the s…
Analysis of the Gibbs sampler for hierarchical inverse problems
Sergios Agapiou, Johnathan M. Bardsley, Omiros Papaspiliopoulos +1
Many inverse problems arising in applications come from continuum models where the unknown parameter is a field. In practice the unknown field is discretized resulting in a problem…
Bayesian Posterior Contraction Rates for Linear Severely Ill-posed Inverse Problems
Sergios Agapiou, Andrew M. Stuart, Yuan-Xiang Zhang
We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian ap…
Posterior Contraction Rates for the Bayesian Approach to Linear Ill-Posed Inverse Problems
Sergios Agapiou, Stig Larsson, Andrew M. Stuart
We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are…