Implicit sampling is a Monte Carlo (MC) method that focuses the computational effort on the region of high probability by first locating this region via numerical optimization and then solving random algebraic equations to explore it. Implicit sampling has been shown to be efficient in online state estimation and filtering (data assimilation) problems; we use it here to estimate a diffusion coe...

Random demodulation based compressive sampling technique is a novel approach that it can break through the Shannon sampling theorem for the sparse signal capturing. A major challenge in the random demodulation based sampling system is the random sequence generation. In this paper, we introduce an approach to generate the high-speed random sequence that meets the incoherence of compressive sampl...

Crowdsourcing platforms are now extensively used for conducting subjective pairwise comparison studies. In this setting, a pairwise comparison dataset is typically gathered via random sampling, either with or without replacement. In this paper, we use tools from random graph theory to analyze these two random sampling methods for the HodgeRank estimator. Using the Fiedler value of the graph as ...

We analyze and compare the efficiency and accuracy of two simulation methods for homogeneous random fields with multiscale resolution. We consider in particular the Fourier-wavelet method and three variants of the Randomization method: (A) without any stratified sampling of wavenumber space, (B) with stratified sampling of wavenumbers with equal energy subdivision, (C) with stratified sampling ...

Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations have arguably surpassed boundary what can be simulated on existing hardware. In this article, we comprehensively review theoretical underpinning in terms complexity and verifiability, as well practical aspects its ...