Related papers: Rare-event Simulation and Efficient Discretization…
How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a "hole" of a certain dimension and depth? Questions of this type are difficult, but in this paper we make progress on questions shedding new…
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…
In this paper we model the loss function of high-dimensional optimization problems by a Gaussian random field, or equivalently a Gaussian process. Our aim is to study gradient descent in such loss functions or energy landscapes and compare…
We develop importance sampling based efficient simulation techniques for three commonly encountered rare event probabilities associated with random walks having i.i.d. regularly varying increments; namely, 1) the large deviation…
With the goal to provide absolute lower bounds for the best possible running times that can be achieved by $(1+\lambda)$-type search heuristics on common benchmark problems, we recently suggested a dynamic programming approach that computes…
In this article we study the tail probability of the mass of critical Gaussian multiplicative chaos (GMC) associated to a general class of log-correlated Gaussian fields in any dimension, including the Gaussian free field (GFF) in dimension…
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…
This article presents a Bayesian inferential method where the likelihood for a model is unknown but where data can easily be simulated from the model. We discretize simulated (continuous) data to estimate the implicit likelihood in a…
Rare event simulation and rare event probability estimation are important tasks within the analysis of systems subject to uncertainty and randomness. Simultaneously, accurately estimating rare event probabilities is an inherently difficult…
Motivated by numerous questions in random geometry, given a smooth manifold $M$, we approach a systematic study of the differential topology of Gaussian random fields (GRF) $X:M\to \mathbb{R}^k$, that we interpret as random variables with…
We propose an extension of the regular Cox's proportional hazards model which allows the estimation of the probabilities of rare events. It is known that when the data are heavily censored at the upper end of the survival distribution, the…
An explicit upper bound on the tail probabilities for the normalized Rademacher sums is given. This bound, which is best possible in a certain sense, is asymptotically equivalent to the corresponding tail probability of the standard normal…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…
This paper presents a novel semiparametric method to study the effects of extreme events on binary outcomes and subsequently forecast future outcomes. Our approach, based on Bayes' theorem and regularly varying (RV) functions, facilitates a…
Threshold selection plays a key role for various aspects of statistical inference of rare events. Most classical approaches tackling this problem for heavy-tailed distributions crucially depend on tuning parameters or critical values to be…
We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated to the probability that the process remains below a…
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…
Finding and sampling rare trajectories in dynamical systems is a difficult computational task underlying numerous problems and applications. In this paper we show how to construct Metropolis- Hastings Monte Carlo methods that can…
We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…