Related papers: Efficient inference and simulation for elliptical …

Flood quantile estimation is of great importance for many engineering studies and policy decisions. However, practitioners must often deal with small data available. Thus, the information must be used optimally. In the last decades, to…

In high-stakes systems such as healthcare, it is critical to understand the causal reasons behind unusual events, such as sudden changes in patient's health. Unveiling the causal reasons helps with quick diagnoses and precise treatment…

Numerical climate models are complex and combine a large number of physical processes. They are key tools in quantifying the relative contribution of potential anthropogenic causes (e.g., the current increase in greenhouse gases) on high…

A proper channel modeling methodology that characterizes the statistics of extreme events is key in the design of a system at an ultra-reliable regime of operation. The strict constraint of ultra-reliability corresponds to the packet error…

Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer models of the likelihood-to-evidence…

We consider the standard thermodynamic processes with constraints, but with additional uncertainty about the control parameters. Motivated by inductive reasoning, we assign prior distribution that provides a rational guess about likely…

In most risk assessment studies, it is important to accurately capture the entire distribution of the multivariate random vector of interest from low to high values. For example, in climate sciences, low precipitation events may lead to…

We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…

A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…

We use the fitted Pareto law to construct an accompanying approximation of the excess distribution function. A selection rule of the location of the excess distribution function is proposed based on a stagewise lack-of-fit testing…

Complex models used to describe biological processes in epidemiology and ecology often have computationally intractable or expensive likelihoods. This poses significant challenges in terms of Bayesian inference but more significantly in the…

We present the elliptical processes -- a family of non-parametric probabilistic models that subsumes the Gaussian process and the Student-t process. This generalization includes a range of new fat-tailed behaviors yet retains computational…

Extreme value functionals of stochastic processes are inverse functionals of the first passage time -- a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for…

$\ell_1$ optimization is a well known heuristic often employed for solving various forms of sparse linear problems. In this paper we look at its a variant that we refer to as the \emph{partial} $\ell_1$ and discuss its mathematical…

Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus existing approaches invariably resort to time-discretisations which inevitably lead to…

Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…

Selective inference (post-selection inference) is a methodology that has attracted much attention in recent years in the fields of statistics and machine learning. Naive inference based on data that are also used for model selection tends…

Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…

When passing from the univariate to the multivariate setting, modelling extremes becomes much more intricate. In this introductory exposition, classical multivariate extreme value theory is presented from the point of view of multivariate…

This paper extends the empirical minimum divergence approach for models which satisfy linear constraints with respect to the probability measure of the underlying variable (moment constraints) to the case where such constraints pertain to…