Related papers: Computing Rare Probabilities of Voltage Collapse
In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo (MLMC) estimators and we provide near optimal weaker conditions under which the CLT…
The problem of robustly reconstructing a large number from its erroneous remainders with respect to several moduli, namely the robust remaindering problem, may occur in many applications including phase unwrapping, frequency detection from…
Stochastic PDE eigenvalue problems are useful models for quantifying the uncertainty in several applications from the physical sciences and engineering, e.g., structural vibration analysis, the criticality of a nuclear reactor or photonic…
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This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions,…
Transient stability assessment of power systems needs to account for increased risk from uncertainties due to the integration of renewables and distributed generators. The uncertain operating condition of the power grid hinders reliable…
Sampling from a log-concave distribution function is one core problem that has wide applications in Bayesian statistics and machine learning. While most gradient free methods have slow convergence rate, the Langevin Monte Carlo (LMC) that…
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This paper aims to proactively diagnose and manage the voltage collapse risks, i.e., the risk of bus voltages violating the safe operational bounds, which can be caused by extreme events and contingencies. We jointly answer two…
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…
Dynamic Fault Trees (DFT) are widely adopted in industry to assess the dependability of safety-critical equipment. Since many systems are too large to be studied numerically, DFTs dependability is often analysed using Monte Carlo…
We obtain local weak limits in probability for Collapsed Branching Processes (CBP), which are directed random networks obtained by collapsing random-sized families of individuals in a general continuous-time branching process. The local…
Monte Carlo maximum likelihood (MCML) provides an elegant approach to find maximum likelihood estimators (MLEs) for latent variable models. However, MCML algorithms are computationally expensive when the latent variables are…
Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…
We investigate the use of Antithetic Variables, Control Variates and Importance Sampling to reduce the statistical errors of option sensitivities calculated with the Likelihood Ratio Method in Monte Carlo. We show how Antithetic Variables…
The main contribution of this work is to construct higher than second order accurate total variation diminishing (TVD) schemes which can preserve high accuracy at non-sonic extrema with out induced local oscillations. It is done in the…
In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection (DBP) method. Each 1D problem consists of recovering a compactly supported function $f \in…
We consider particle systems (also known as point processes) on the line and in the plane, and are particularly interested in "hole" events, when there are no particles in a large disk (or some other domain). We survey the extensive work on…
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We characterize the complex, heavy-tailed probability distribution functions (pdf) describing the response and its local extrema for structural systems subjected to random forcing that includes extreme events. Our approach is based on the…