Derives non-asymptotic error bounds for standard, defensive, and self-normalized importance sampling with random KDE proposals from geometrically ergodic Markov chains, separating n^{-1/2} Monte Carlo error from MIAE/MISE proposal error.
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KDE-AIS trains a Gaussian process and kernel density surrogate from shared evaluations to build an adaptive importance sampling proposal that converges to the zero-variance optimum for efficient failure probability estimation.
Niching importance sampling yields a robust probability-of-failure estimator that avoids degeneracy on multi-modal performance functions by integrating evolutionary niching with importance sampling.
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Error Bounds for Importance Sampling with Estimated Proposal Distributions
Derives non-asymptotic error bounds for standard, defensive, and self-normalized importance sampling with random KDE proposals from geometrically ergodic Markov chains, separating n^{-1/2} Monte Carlo error from MIAE/MISE proposal error.
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Surrogate-Guided Adaptive Importance Sampling for Failure Probability Estimation
KDE-AIS trains a Gaussian process and kernel density surrogate from shared evaluations to build an adaptive importance sampling proposal that converges to the zero-variance optimum for efficient failure probability estimation.
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Niching Importance Sampling for Multi-modal Rare-event Simulation
Niching importance sampling yields a robust probability-of-failure estimator that avoids degeneracy on multi-modal performance functions by integrating evolutionary niching with importance sampling.