# Publications

Bayes is Optimal,” ICES Report, vol. 15, no. 04, Submitted.

, “Emulation of higher-order tensors in manifold Monte Carlo methods for Bayesian Inverse Problems,” Submitted.

, “FEM-Based Discretization-Invariant MCMC Methods for PDE-constrained Bayesian Inverse Problems,” Submitted.

, “From Rankine-Hugoniot Condition to a Constructive Derivation of HDG Methods,” Lecture Notes in Computational Science and Engineering, Submitted.

, “ , “A Randomized Misfit Approach for Data Reduction in Large-Scale Inverse Problems,” SIAM Special Edition, Submitted.

, “Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method,” Journal of Scientific Computing, no. 63, pp. 138--162, 2015.

, “From Godunov to A Unified Hybridized Discontinuous Galerkin Framework,” Journal of Computational Physics, no. 295, pp. 114-146, 2015.

, “A Randomized Misfit Approach for Data Reduction in Large-Scale Inverse Problems,” SIAM CSE Conference. 2015.

, “A Scalable MAP Solver for Bayesian Inverse Problems with Besov Priors, Inverse Problems and Imaging,” Inverse Problems and Imaging, no. 9, pp. 27--53, 2015.

, “A PDE-constrained Optimization Approach to the Discontinuous Petrov-Galerkin Method with a Trust Region Inexact Newton-CG Solver,” Computational Methods Applied Mechanical Engineering, no. 278, pp. 20--40, 2014.

, “Solving Large-scale PDE-Constrained Bayesian Inverse Problems With Riemann Manifold Hamiltonian Monte Carlo,” Inverse Problems, Special Issue, no. 114014, pp. 30, 2014.

, “The DPG Method for the Stokes Problem, Computers & Mathematics with Applications. 67, 2014, pp. 966–995.

, Robust DPG method for convection-dominated diffusion problems II: a natural in flow condition, Computers & Mathematics with Applications. 67, 2014, pp. 771–795.

, An Analysis of Infinite Dimensional Bayesian Inverse Shape Acoustic Scattering and its Numerical Approximation,” SIAM Journal on Uncertainty Quantification, no. 2, pp. 203--222, 2014.

, “Analysis of the Hessian for Inverse Scattering Problems Part III: Inverse Medium Scattering of Electromagnetic Waves in Three Dimensions,” Inverse Problems and Imaging, vol. 7, pp. 1139–1155, 2013.

, “A computational framework for infinite-dimensional Bayesian inverse problems Part I: The linearized case, with application to global seismic inversion,” SIAM Journal on Scientific Computing, vol. 35, pp. A2494–A2523, 2013.

, “Constructively Well-Posed Approximation Methods with Unity Inf-Sup and Continuity Constants for Partial Differential Equations,” Mathematics of Computation, vol. 82, no. 284, pp. 1923–1952, 2013.

, “A Unified Discontinuous Petrov-Galerkin Method and its Analysis for Friedrichs' Systems,” SIAM Journal on Numerical Analysis, vol. 51, no. 4, pp. 1933–1958, 2013.

, “A Gentle Tutorial on Statistical Inversion using the Bayesian Paradigm,” ICES Report 12-18, 2012.

, “