51 citations · 289 across the 43 of their papers we have counts for
10 papers · 1 filter
Statistical inverse learning problems with random observations
Abhishake Rastogi, Tapio Helin, Nicole Mücke
We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regulariza…
Least squares approximations in linear statistical inverse learning problems
Tapio Helin
Statistical inverse learning aims at recovering an unknown function from randomly scattered and possibly noisy point evaluations of another function , connected to via a…
Stability estimates for the expected utility in Bayesian optimal experimental design
Duc-Lam Duong, Tapio Helin, Jose Rodrigo Rojo-Garcia
We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prov…
Hyperparameter Estimation in Bayesian MAP Estimation: Parameterizations and Consistency
Matthew M. Dunlop, Tapio Helin, Andrew M. Stuart
The Bayesian formulation of inverse problems is attractive for three primary reasons: it provides a clear modelling framework; means for uncertainty quantification; and it allows f…
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…
Generalized modes in Bayesian inverse problems
Christian Clason, Tapio Helin, Remo Kretschmann +1
Uncertainty quantification requires efficient summarization of high- or even infinite-dimensional (i.e., non-parametric) distributions based on, e.g., suitable point estimates (mod…