55 citations · 216 across the 24 of their papers we have counts for
29 papers
The Quality of Lattice Sequences for Arbitrary Sample Size
Larysa Matiukha, Yuhan Ding, Fred J. Hickernell
Extensible lattices are a common choice of nodes for approximating multidimensional integrals by a sample mean, typically using sample sizes of the form for a prime base…
Fast multitask Gaussian processes, with application to surrogate modeling of the quark-gluon plasma
Aleksei G. Sorokin, Pieterjan Robbe, Yen-Chun Liu +2
Gaussian processes (GPs) are broadly used for the surrogate modeling of computer experiments with reliable uncertainty quantification. Our motivating application comes from the stu…
Fast Bayesian Multilevel Quasi-Monte Carlo
Aleksei G. Sorokin, Pieterjan Robbe, Gianluca Geraci +2
Existing multilevel quasi-Monte Carlo (MLQMC) methods often rely on multiple independent randomizations of a low-discrepancy (LD) sequence to estimate statistical errors on each le…
Empirical Bernstein and betting confidence intervals for randomized quasi-Monte Carlo
Aadit Jain, Fred J. Hickernell, Art B. Owen +1
Randomized quasi-Monte Carlo (RQMC) methods estimate the mean of a random variable by sampling an integrand at equidistributed points. For scrambled digital nets, the resulting…
Quasi-Monte Carlo Methods: What, Why, and How?
Fred J. Hickernell, Nathan Kirk, Aleksei G. Sorokin
Many questions in quantitative finance, uncertainty quantification, and other disciplines are answered by computing the population mean, , where instances of $Y:…
Challenges in Developing Great Quasi-Monte Carlo Software
Sou-Cheng T. Choi, Yuhan Ding, Fred J. Hickernell +2
Quasi-Monte Carlo (QMC) methods have developed over several decades. With the explosion in computational science, there is a need for great software that implements QMC algorithms.…
Computationally Efficient and Error Aware Surrogate Construction for Numerical Solutions of Subsurface Flow Through Porous Media
Aleksei G. Sorokin, Aleksandra Pachalieva, Daniel O'Malley +3
Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between inj…
A unified treatment of tractability for approximation problems defined on Hilbert spaces
Onyekachi Emenike, Fred J. Hickernell, Peter Kritzer
A large literature specifies conditions under which the information complexity for a sequence of numerical problems defined for dimensions grows at a moderate rate,…
Quasi-Monte Carlo Software
Sou-Cheng T. Choi, Fred J. Hickernell, R. Jagadeeswaran +2
Practitioners wishing to experience the efficiency gains from using low discrepancy sequences need correct, robust, well-written software. This article, based on our MCQMC 2020 tut…
Is a Transformed Low Discrepancy Design Also Low Discrepancy?
Yiou Li, Lulu Kang, Fred J. Hickernell
Experimental designs intended to match arbitrary target distributions are typically constructed via a variable transformation of a uniform experimental design. The inverse distribu…
Adaptive Approximation for Multivariate Linear Problems with Inputs Lying in a Cone
Yuhan Ding, Fred J. Hickernell, Peter Kritzer +1
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorith…
Comment on "Probabilistic Integration: A Role in Statistical Computation?"
Fred J. Hickernell, R. Jagadeeswaran
Probabilistic integration provides a criterion for stopping a simulation when a specified error tolerance is satisfied with high confidence. We comment on some of the modeling assu…
Exponential tractability of linear tensor product problems
Fred J. Hickernell, Peter Kritzer, Henryk Wozniakowski
In this article we consider the approximation of compact linear operators defined over tensor product Hilbert spaces. Necessary and sufficient conditions on the singular values of…
An Adaptive Algorithm Employing Continuous Linear Functionals
Yuhan Ding, Fred J. Hickernell, Lluís Antoni Jiménez Rugama
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic,…
Fast Automatic Bayesian Cubature Using Lattice Sampling
R. Jagadeeswaran, Fred J. Hickernell
Automatic cubatures approximate multidimensional integrals to user-specified error tolerances. For high dimensional problems, it makes sense to fix the sampling density but determi…
Adaptive Quasi-Monte Carlo Methods for Cubature
Fred J. Hickernell, Lluís Antoni Jiménez Rugama, Da Li
High dimensional integrals can be approximated well by quasi-Monte Carlo methods. However, determining the number of function values needed to obtain the desired accuracy is diffic…
The Trio Identity for Quasi-Monte Carlo Error
Fred J. Hickernell
Monte Carlo methods approximate integrals by sample averages of integrand values. The error of Monte Carlo methods may be expressed as a trio identity: the product of the variation…
Local Adaption for Approximation and Minimization of Univariate Functions
Sou-Cheng T. Choi, Yuhan Ding, Fred J. Hickernell +1
Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algori…
GAIL---Guaranteed Automatic Integration Library in MATLAB: Documentation for Version 2.1
Sou-Cheng T. Choi, Yuhan Ding, Fred J. Hickernell +5
Automatic and adaptive approximation, optimization, or integration of functions in a cone with guarantee of accuracy is a relatively new paradigm. Our purpose is to create an open-…
Guaranteed Monte Carlo Methods for Bernoulli Random Variables
Lan Jiang, Fred J. Hickernell
Simple Monte Carlo is a versatile computational method with a convergence rate of . It can be used to estimate the means of random variables whose distributions are un…
Tractability of the function approximation problem in terms of the kernel's shape and scale parameters
Xuan Zhou, Fred J. Hickernell
This article studies the problem of approximating functions belonging to a Hilbert space with a reproducing kernel of the form $$\tilde K_d(\boldsymbol x,\boldsymbol…
Adaptive Multidimensional Integration Based on Rank-1 Lattices
Lluís Antoni Jiménez Rugama, Fred J. Hickernell
Quasi-Monte Carlo methods are used for numerically integrating multivariate functions. However, the error bounds for these methods typically rely on a priori knowledge of some semi…
Reliable Adaptive Cubature Using Digital Sequences
Fred J. Hickernell, Lluís Antoni Jiménez Rugama
Quasi-Monte Carlo cubature methods often sample the integrand using Sobol' (or other digital) sequences to obtain higher accuracy than IID sampling. An important question is how to…
The Cost of Deterministic, Adaptive, Automatic Algorithms: Cones, Not Balls
Nicholas Clancy, Yuhan Ding, Caleb Hamilton +2
Automatic numerical algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. The computational cost is…