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Most current risk assessment for complex extreme events relies on catalogues of similar events, either historical or generated artificially. In the latter, no existing methods produce completely new events with mathematically justified extrapolation above ...
This thesis addresses statistical inference for the resolution of inverse problems. Our work is motivated by the recent trend whereby classical linear methods are being replaced by nonlinear alternatives that rely on the sparsity of naturally occurring sig ...
We consider the estimation of an independent and identically distributed (i.i.d.) (possibly non-Gaussian) vector x is an element of R-n from measurements y is an element of R-m obtained by a general cascade model consisting of a known linear transform foll ...
In this thesis, we treat robust estimation for the parameters of the Ornstein–Uhlenbeck process, which are the mean, the variance, and the friction. We start by considering classical maximum likelihood estimation. For the simulation study, where we also in ...
The increasing interest in using statistical extreme value theory to analyse environmental data is mainly driven by the large impact extreme events can have. A difficulty with spatial data is that most existing inference methods for asymptotically justifie ...
Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from high-dimensional distributions in Statistics and Machine learning. HMC is known to run very efficiently in practice and its popular second-order "leapfrog" implementation has long bee ...
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the performance of pop ...
Max-stable processes arise as the only possible nontrivial limits for maxima of affinely normalized identically distributed stochastic processes, and thus form an important class of models for the extreme values of spatial processes. Until recently, infere ...
Global warming is expected to intensify the hydrologic cycle. Documenting whether significant changes in the extreme precipitation regimes have already happened is consequently one of the challenging topics in climatic research. The high natural variabilit ...
The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based estimator for the ...
