Related papers: On the connection between orthant probabilities an…
In this paper we address the problem of the calculation of the mean first passage time (MFPT) on generic graphs. We focus in particular on the mean first passage time on a node 's' for a random walker starting from a generic, unknown, node…
We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…
Gradient-based (a.k.a. `first order') optimization algorithms are routinely used to solve large scale non-convex problems. Yet, it is generally hard to predict their effectiveness. In order to gain insight into this question, we revisit the…
Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with…
We have developed a method to determine the transient surface density and transient rate for any given survey, using Monte-Carlo simulations. This method allows us to determine the transient rate as a function of both the flux and the…
We develop methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in applications with market frictions. Pivotal to our approach is that our methods operate on…
We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a personal computer. The…
We use the concept of excursions for the prediction of random variables without any moment existence assumptions. To do so, an excursion metric on the space of random variables is defined which appears to be a kind of a weighted…
Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…
Markov chain Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper a method is proposed to overcome this difficulty.…
We construct a set of instances of 3SAT which are not solved efficiently using the simplest quantum adiabatic algorithm. These instances are obtained by picking random clauses all consistent with two disparate planted solutions and then…
First-passage probability estimation of high-dimensional nonlinear stochastic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel…
Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models…
This paper provides an exact simulation algorithm for the sampling from the joint law of the first-passage time, the undershoot and the overshoot of a subordinator crossing a non-increasing boundary. We prove that the running time of this…
The mean first-passage time (MFPT) is one standard measure for the reaction time in thermally activated barrier-crossing processes. While the relationship between MFPTs and phenomenological rate coefficients is known for systems that…
The inverse first-passage time problem determines a boundary such that the first-passage time of a Wiener process to this boundary has a given distribution. An approximation which is based on the starting value of the boundary to a smooth…
We derive a Sturm-Liouville system of equations for the exact calculation of the survival probability in first-passage time problems. This system is the one associated with the Wiener-Hopf integral equation obtained from the theory of…
We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…