Related papers: Rare Event Simulation for Steady-State Probabiliti…
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…
This paper considers the classical problem of sampling with Monte Carlo methods a target rare event distribution defined by a score function that is very expensive to compute. We assume we can build using evaluations of the true score, an…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective…
Transitional localised turbulence in shear flows is known to either decay to an absorbing laminar state or proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number…
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 consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…
Standard rare-event simulation techniques require exact distributional specifications, which limits their effectiveness in the presence of distributional uncertainty. To address this, we develop a novel framework for estimating rare-event…
This article focuses, in the context of epidemic models, on rare events that may possibly correspond to crisis situations from the perspective of Public Health. In general, no close analytic form for their occurrence probabilities is…
Rare events in Stochastic Vector Addition System (VAS) are of significant interest because, while extremely unlikely, they may represent undesirable behavior that can have adverse effects. Their low probabilities and potentially extremely…
Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. This leads in some cases to symmetry-broken space-time…
We here consider the subset simulation method which approaches a failure event using a decreasing sequence of nested intermediate failure events. The method resembles importance sampling, which actively explores a probability space by…
By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the model parameters. Hence, understanding the sensitivity of the…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
An important step in the design of autonomous systems is to evaluate the probability that a failure will occur. In safety-critical domains, the failure probability is extremely small so that the evaluation of a policy through Monte Carlo…
Considering the issue of estimating small probabilities p, ie. measuring a rare domain F = {x | g(x) > q} with respect to the distribution of a random vector X, Multilevel Splitting strategies (also called Subset Simulation) aim at writing…
Diffusion processes with small noise conditioned to reach a target set are considered. The AMS algorithm is a Monte Carlo method that is used to sample such rare events by iteratively simulating clones of the process and selecting…
We explore past and recent developments in rare-event probability estimation with a particular focus on a novel Monte Carlo technique Empirical Likelihood Maximization (ELM). This is a versatile method that involves sampling from a sequence…
Online planning in Markov Decision Processes (MDPs) enables agents to make sequential decisions by simulating future trajectories from the current state, making it well-suited for large-scale or dynamic environments. Sample-based methods…
Adaptive Multilevel Splitting (AMS for short) is a generic Monte Carlo method for Markov processes that simulates rare events and estimates associated probabilities. Despite its practical efficiency, there are almost no theoretical results…