Related papers: Rare Event Simulation for Steady-State Probabiliti…
We consider the problem of extinction processes on random networks with a given structure. For sufficiently large well-mixed populations, the process of extinction of one or more state variable components occurs in the tail of the…
We propose a class of discrete state sampling algorithms based on Nesterov's accelerated gradient method, which extends the classical Metropolis-Hastings (MH) algorithm. The evolution of the discrete states probability distribution governed…
In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Feynman--Kac…
Algorithms for rare event complex systems simulations are proposed. Compressed Sensing (CS) has {\it revolutionized} our understanding of limits in signal recovery and has forced us to re-define Shannon-Nyquist sampling theorem for sparse…
The bifurcation method is a way to do rare event sampling -- to estimate the probability of events that are too rare to be found by direct simulation. We describe the bifurcation method and use it to estimate the transition rate of a double…
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…
Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard…
High intermittent renewable penetration in the energy mix presents challenges in robustness for the management of power systems' operation. If a tail realization of the distribution of weather yields a prolonged period of time during which…
The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary…
A common problem that affects simulations of complex systems within the computational physics and chemistry communities is the so-called sampling problem or rare event problem where proper sampling of energy landscapes is impeded by the…
We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…
Rare properties remain a challenge for statistical model checking (SMC) due to the quadratic scaling of variance with rarity. We address this with a variance reduction framework based on lightweight importance splitting observers. These…
Accurate and efficient estimation of rare events probabilities is of significant importance, since often the occurrences of such events have widespread impacts. The focus in this work is on precisely quantifying these probabilities, often…
In this paper, we propose a sequential directional importance sampling (SDIS) method for rare event estimation. SDIS expresses a small failure probability in terms of a sequence of auxiliary failure probabilities, defined by magnifying the…
Article describes the results of the development and using of Rare-Event Monte-Carlo Simulation Algorithms for Dynamic Fault Trees Estimation. For Fault Trees estimation usually analytical methods are used (Minimal Cut sets, Markov Chains,…
The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell biophysics. Yet, exact simulation methods, for the…
In this paper, we present a novel iterative Monte Carlo method for approximating the stationary probability of a single state of a positive recurrent Markov chain. We utilize the characterization that the stationary probability of a state…
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…
The analysis of extremes in climate models is hindered by the lack of statistics due to the computational costs required to run simulations long enough to sample rare events. We demonstrate how rare event algorithms can improve the…
In this work, we propose an algorithm to simulate rare events for electronic circuit design. Our approach heavily relies on a smart use of importance sampling, which enables us to tackle probabilities of the magnitude 10 --10. Not only can…