Optimal Monte Carlo integration on closed manifolds
From MaRDI portal
Publication:2302449
DOI10.1007/s11222-019-09894-wzbMath1436.62724arXiv1707.04723OpenAlexW2784596296MaRDI QIDQ2302449
Chris J. Oates, Martin Ehler, Manuel Gräf
Publication date: 26 February 2020
Published in: Statistics and Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1707.04723
Statistics on manifolds (62R30) Bayesian inference (62F15) Monte Carlo methods (65C05) Global Riemannian geometry, including pinching (53C20) Approximate quadratures (41A55)
Related Items
A Riemann-Stein kernel method ⋮ Recovery of Sobolev functions restricted to iid sampling ⋮ Spherical Framelets from Spherical Designs ⋮ Quadrature points via heat kernel repulsion ⋮ Symmetry exploits for Bayesian cubature methods ⋮ A modern retrospective on probabilistic numerics ⋮ Sampling, Marcinkiewicz-Zygmund inequalities, approximation, and quadrature rules
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions
- Points on manifolds with asymptotically optimal covering radius
- Numerical cubature on scattered data by radial basis functions
- Optimal importance sampling for the approximation of integrals
- Tractability of multivariate problems. Volume II: Standard information for functionals.
- Theory of function spaces II
- New averaging technique for approximating weighted integrals
- Some current issues in quasi-Monte Carlo methods
- Average-case analysis of numerical problems
- Convergence rates for a class of estimators based on Stein's method
- Heat kernel generated frames in the setting of Dirichlet spaces
- Generalized Zernike or disc polynomials
- A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel
- Monte Carlo with determinantal point processes
- Gaussian bounds for the weighted heat kernels on the interval, ball, and simplex
- Convergence analysis of deterministic kernel-based quadrature rules in misspecified settings
- Probabilistic integration: a role in statistical computation?
- Localized polynomial frames on the ball
- Gaussian measure in Hilbert space and applications in numerical analysis
- Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
- QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere
- Estimates of derivatives of the heat kernel on a compact Riemannian manifold
- Orthogonal Polynomials and Cubature Formulae on Spheres and on Balls
- Efficient Quadrature Rules for Illumination Integrals: From Quasi Monte Carlo to Bayesian Monte Carlo
- The Covering Radius of Randomly Distributed Points on a Manifold
- Kernel Mean Embedding of Distributions: A Review and Beyond
- Fully Symmetric Kernel Quadrature
- Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians
- Quadrature rules and distribution of points on manifolds
- A Monte Carlo Method for Integration of Multivariate Smooth Functions
- Cubature, Approximation, and Isotropy in the Hypercube
- Multivariate polynomial approximation in the hypercube
- A Comparison of Popular Point Configurations on $\mathbb{S}^2$
- Random Point Sets on the Sphere—Hole Radii, Covering, and Separation
- A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines
- Control Functionals for Monte Carlo Integration
- Orthogonal polynomials and cubature formulae on balls, simplices, and spheres
- Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces
