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Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a data set has been collected under normal…
Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations…
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
Drees and Rootz\'en [2010] have proven central limit theorems (CLT) for empirical processes of extreme values cluster functionals built from $\beta$-mixing processes. The problem with this family of $\beta$-mixing processes is that it is…
Estimating the model evidence - or mariginal likelihood of the data - is a notoriously difficult task for finite and infinite mixture models and we reexamine here different Monte Carlo techniques advocated in the recent literature, as well…
Multilevel Splitting methods, also called Sequential Monte-Carlo or \emph{Subset Simulation}, are widely used methods for estimating extreme probabilities of the form $P[S(\mathbf{U}) > q]$ where $S$ is a deterministic real-valued function…
Let $X$ be a $2$-dimensional subshift of finite type generated by a finite set of forbidden blocks (of finite size). We give an algorithm for generating the elements of the shift space using sequence of finite matrices (of increasing size).…
We consider empirical multi-dimensional Rare Events Point Processes that keep track both of the time occurrence of extremal observations and of their severity, for stochastic processes arising from a dynamical system, by evaluating a given…
Factor model is an appealing and effective analytic tool for high-dimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of…
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the…
It is shown by Monte Carlo method that the finite size scaling (FSS) holds in the two dimensional random-coupled Ising ferromagnet. It is also demonstrated that the form of universal FSS function constructed via novel FSS scheme depends on…
We present large scale simulations of a stochastic sandpile model in two dimensions. We use moments analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. The general picture…
In this paper, we study numerical approximations of the ground states in finite temperature density functional theory. We formulate the problem with respect to the density matrices and justify the convergence of the finite dimensional…
Variational methods are a common approach for computing properties of ground states but have not yet found analogous success in finite temperature calculations. In this work we develop a new variational finite temperature algorithm (VAFT)…
It is shown that superefficient Monte Carlo computations can be carried out by using chaotic dynamical systems as non-uniform random-number generators. Here superefficiency means that the expectation value of the square of the error…
Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to…
In recent years dynamical systems (of deterministic and stochastic nature), describing many models in mathematics, physics, engineering and finances, become more and more complex. Numerical analysis narrowed only to deterministic algorithms…
Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. $r$-Pareto processes are mathematically…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…