138 citations · 788 across the 67 of their papers we have counts for
5 papers · 2 filters
Multilevel higher order Quasi-Monte Carlo Bayesian Estimation
Josef Dick, Robert N. Gantner, Quoc T. Le Gia +1
We propose and analyze deterministic multilevel approximations for Bayesian inversion of operator equations with uncertain distributed parameters, subject to additive Gaussian meas…
Lattice based integration algorithms: Kronecker sequences and rank-1 lattices
Josef Dick, Friedrich Pillichshammer, Kosuke Suzuki +2
We prove upper bounds on the order of convergence of lattice based algorithms for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homo…
On the optimal order of integration in Hermite spaces with finite smoothness
Josef Dick, Christian Irrgeher, Gunther Leobacher +1
We study the numerical approximation of integrals over with respect to the standard Gaussian measure for integrands which lie in certain Hermite spaces of functions.…
Higher order Quasi-Monte Carlo integration for Bayesian Estimation
Josef Dick, Robert N. Gantner, Quoc T. Le Gia +1
We analyze combined Quasi-Monte Carlo quadrature and Finite Element approximations in Bayesian estimation of solutions to countably-parametric operator equations with holomorphic d…
Construction of interlaced polynomial lattice rules for infinitely differentiable functions
Josef Dick, Takashi Goda, Kosuke Suzuki +1
We study multivariate integration over the -dimensional unit cube in a weighted space of infinitely differentiable functions. It is known from a recent result by Suzuki that the…