Large sample properties of simulations using latin hypercube sampling

By Michael L. Stein. 1987

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Citations in the corpus

Physics-Informed Neural Networks for Cardiac Activation Mapping (2020, methodology): “For the two-dimensional benchmark problem, we randomly sampleNmb points using a Latin hypercube design [27] and use them as collocation points.”
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations (2017, methodology): “ randomly sampled collocation points used to enforce equation (5) inside the solution domain. All randomly sampled point locations were generated using a space lling Latin Hypercube Sampling strategy [23]. Here our goal is to infer the entire spatio-temporal solution h(t;x) of the Schrodinger equati”
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations (2017, methodology): “All randomly sampled point locations were generated using a space ﬁlling Latin Hypercube Sampling strategy [23].”
On the asymptotic distribution of scrambled net quadrature (2003, methodology): “An objective of many computer experiments [see, e.g., McKay, Conover and Beckman (1979), Stein (1987), Owen (1992a) and Tang (1993)] is to estimate µ = Ef (X) = ∫ [0,1)s f (x) dx(1) using a fixed number of function evaluations.”
Monte Carlo sampling-based methods for stochastic optimization (2014, unknown): “Stein [231] and Owen [178] show”
Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN (2021, methodology): “The initial and Dirichlet periodic boundary data are obtained by Latin hypercube sampling [31].”
Latin hypercube lattice sample selection strategy for correlated random hydraulic conductivity fields (2003, methodology): “The LHS scheme has been shown to be more efficient in obtaining an asymptotic representation of the variance of the estimate than simple random sampling [Stein, 1987].”
Short survey Scaling-up crop models for climate variability applications $ (2000, background): “Latin hypercube sampling (McKay et al., 1979; Stein, 1987) oers a more ecient alternative to independent random sampling.”
Estimating Mean Dimensionality of Analysis of Variance Decompositions (2006, background): “Stein (1987) showed that Latin hypercube sampling remains an effective integration tool for functions that are nearly additive.”
Some issues in uncertainty quantification and parameter tuning: a case study of convective parameterization scheme in the WRF regional climate model (2011, background): “…Kirkpatrick et al., 1983; Sen and Stoffa, 1996), Monte Carlo or Quasi Monte Carlo (QMC), (Moskowitz and Caflisch, 1996), Latin Hypercube selection (Stein, 1987), Multiple Very Fast Simulated Annealing (MVFSA) (Ingber, 1989; Jackson et al., 2004), among others (Tierney and Mira, 1999; Haario et…”
Bayesian calibration of building energy models with large datasets (2017, methodology): “To learn about the calibration parameters t, m simulations with different values of t were run, where each simulation is run at the same observable input factors x. Maximin latin hypercube sampling (Stein, 1987) was used to generate different values of t for each simulation.”
A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics (2004, unknown): “Simulation and sampling methods, such as direct Monte Carlo simulation [21], quasi-Monte Carlo simulation [22–24], importance sampling [25, 26], directional simulation [27, 28], and others [29–32], are well known in the statistics and reliability literature.”
Fast Numerical Methods for Stochastic Computations: A Review (2009, unknown): “[50, 74]), quasi Monte Carlo (cf.”
Data-Driven Evolutionary Optimization: An Overview and Case Studies (2019, methodology): “Most on-line data-driven EAs start with generating a number of candidate solutions using a design of experiment technique, e.g., LHS [87].”