期刊: SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2021; 9 (1)
We interpret steady linear statistical inverse problems as artificial dynamic systems with white noise and introduce a stochastic differential equatio......
期刊: SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2021; 9 (2)
In this paper, we propose a lattice Boltzmann method (LBM) for stochastic convection-diffusion equations (CDEs). The stochastic Galerkin method is emp......
期刊: SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2020; 8 (3)
Particle filtering (PF) is an often used method to estimate the states of dynamical systems. A major limitation of the standard PF method is that the ......
期刊: SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2020; 8 (3)
All observable phenomena can be described by alternative mathematical models, which vary in their fidelity and computational cost. Selection of an app......
期刊: SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2020; 8 (3)
Design of systems based on computer simulations is prevalent. An important idea to improve design quality, called robust parameter design (RPD), is to......
期刊: SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2020; 8 (4)
Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions under which the act......
期刊: SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2019; 7 (2)
We consider the inverse problem of parameter estimation in a diffuse interface model for tumor growth. The model consists of a fourth-order Cahn-Hilli......
期刊: SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2018; 6 (2)
How to incorporate the gradient information of a computer code is an important problem in computer experiments. The gradient-enhanced Gaussian process......
期刊: SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2018; 6 (1)
For the general partially observed framework of Markov processes with marked point process observations proposed in [G. X. Hu, D. R. Kuipers, and Y. Z......
期刊: SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2018; 6 (1)
We propose a general partially observed framework of Markov processes with marked point process observations for ultrahigh frequency (UHF) data. The m......
期刊: SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2017; 5 (1)
The preconditioned Crank-Nicolson (pCN) method is a Markov Chain Monte Carlo (MCMC) scheme, specifically designed to perform Bayesian inferences in fu......