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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A New Uncertainty Importance Measure
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An omnitree that bisects only selected dimensions per node can raise dyadic AMR convergence by up to the dimension count d for strongly anisotropic problems; on 4,166 shapes it improved mean convergence 1.5x versus octrees.
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