Related papers: Rare-event Simulation and Efficient Discretization…

For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and…

Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…

Random field excursions is an increasingly vital topic within data analysis in medicine, cosmology, materials science, etc. This work is the first detailed study of their Betti numbers in the so-called `sparse' regime. Specifically, we…

We develop a recently proposed importance-sampling Monte Carlo algorithm for sampling rare events and quenched variables in random disordered systems. We apply it to a two dimensional bond-diluted Ising model and study the Griffiths…

Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F.…

We study the high excursion probability of a centered Gaussian field on a square. Writing \(\sigma\) and \(r\) for its standard deviation and correlation function, we assume that \(\sigma\) has a unique maximum at the corner…

We consider the problem of efficient simulation estimation of the density function at the tails, and the probability of large deviations for a sum of independent, identically distributed, light-tailed and non-lattice random vectors. The…

Phenomenologically interesting scalar potentials are highly atypical in generic random landscapes. We develop the mathematical techniques to generate constrained random potentials, i.e. Slepian models, which can globally represent…

A procedure to include the uncertainty on the background estimate for upper limit calculations using Poissonian sampling is presented for the case where a Gaussian assumption on the uncertainty can be made. Under that hypothesis an analytic…

Programs with randomization constructs is an active research topic, especially after the recent introduction of martingale-based analysis methods for their termination and runtimes. Unlike most of the existing works that focus on proving…

In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…

We consider the stochastic gradient method with random reshuffling ($\mathsf{RR}$) for tackling smooth nonconvex optimization problems. $\mathsf{RR}$ finds broad applications in practice, notably in training neural networks. In this work,…

This article describes a method for using optimization to derive efficient independent transition functions for Markov chain Monte Carlo simulations. Our interest is in sampling from a posterior density $\pi(x)$ for problems in which the…

Estimating the left tail of quadratic forms in Gaussian random vectors is of major practical importance in many applications. In this letter, we propose an efficient importance sampling estimator that is endowed with the bounded relative…

Let g : $\Omega$ = [0, 1] d $\rightarrow$ R denote a Lipschitz function that can be evaluated at each point, but at the price of a heavy computational time. Let X stand for a random variable with values in $\Omega$ such that one is able to…

Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point…

We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy…

Because the stochastic calculus yields rarely random variables with laws defined by explicit closed formulas, probabilistic numerical computations are done most often by simulation. The simulation by the shift, whose field of application is…

This paper is concerned with the asymptotic analysis of sojourn times of random fields with continuous sample paths. Under a very general framework we show that there is an interesting relationship between tail asymptotics of sojourn times…

This paper considers the robust and efficient implementation of Gaussian process regression with a Student-t observation model. The challenge with the Student-t model is the analytically intractable inference which is why several…