### Published (appeared/accepted)

*A Stochastic Inverse Problem Framework for Determination of Model Upscaling*, N. Panda, T. Butler, D. Estep, L. Graham, and C. Dawson, Status: accepted June 2017*A Measure-Theoretic Interpretation of Sample Based Numerical Integration with Applications to Inverse and Prediction Problems Under Uncertainty*, T. Butler, L. Graham, S. Mattis, and S. Walsh, Status: accepted April 2017*A Measure-Theoretic Algorithm for Estimating Bottom Friction in a Coastal Inlet: Case Study of Bay St. Louis during Hurricane Gustav (2008)*, L. Graham, T. Butler, S. Walsh, C. Dawson, J.J. Westerink, Monthly Weather Review, Volume 145, No. 3, (2017), pp. 929-954*Parameter estimation and prediction for groundwater contamination based on measure theory*, S. Mattis, T. Butler, C. Dawson, D. Estep, V.V. Vesselinov, Water Resources Research, Volume 51, (2015), pp. 7608-7629*Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models*, T. Butler, L. Graham, C. Dawson, D. Estep, J.J. Westerink, Advances in Water Resources, Volume 78, (2015), pp. 60-79*Quantifying Uncertainty in Material Damage from Vibrational Data*, T. Butler, A. Huhtala, M. Juntunen, Journal of Computational Physics, Volume 283, (2015), pp. 414–435*A comparison of ensemble Kalman filters for short range forecasting*, M.U. Altaf, T. Butler, T. Mayo, X. Luo, C. Dawson, A.W. Heemink, I. Hoteit, Monthly Weather Review, Volume 142, No. 8, (2014), pp. 2899–2914*A measure-theoretic computational method for inverse sensitivity problems III: Multiple Quantities of Interest*, T. Butler, D. Estep, S. Tavener, C. Dawson, J.J. Westerink, SIAM/ASA Journal on Uncertainty Quantification, Vol. 2, (2014), pp. 174-202*Data Assimilation within the Advanced Circulation (ADCIRC) Modeling Framework for the Estimation of Manning's Friction Coefficient*, T. Mayo, T. Butler, C. Dawson, I. Hoteit, Ocean Modelling, Vol. 76, (2014), pp. 43-58*Propagation of uncertainties using improved surrogate models*, T. Butler, C. Dawson, and T. Wildey, SIAM/ASA Journal on Uncertainty Quantification, Vol. 1, (2013), pp. 164-191*Improving Short-Range Ensemble Kalman Storm Surge Forecasting Using Robust Adaptive Inflation*, M.U. Altaf, T. Butler, X. Luo, C. Dawson, T. Mayo, I. Hoteit, Monthly Weather Review, Vol. 141, No. 8, (2013), pp. 2705-2720*A numerical method for solving a stochastic inverse problem for parameters*, T. Butler and D. Estep, Annals of Nuclear Energy, Vol. 52, (2013), pp. 86 - 94*Data Assimilation within the Advanced Circulation (ADCIRC) Modeling Frameowork for Hurricane Storm Surge Forecasting*, T. Butler, M.U. Altaf, C. Dawson, I. Hoteit, X. Luo, and T. Mayo, Monthly Weather Review, Vol. 140, No. 7. (2012), pp. 2215-2231*Reparameterization for statistical state estimation applied to differential equations*, T. Butler, M. Juntunen, Journal of Computational Physics, Vol. 231, (2012), pp. 2641-2654*A posteriori error analysis of parameterized linear systems using spectral methods*, T. Butler, P. Constantine, T. Wildey, SIAM Journal on Matrix Analysis and Applications, Vol. 33, (2012), pp. 195-209*A computational measure-theoretic approach to inverse sensitivity problems II: A posteriori error analysis*, T. Butler, D. Estep, J. Sandelin, SIAM Journal on Numerical Analysis, Vol. 50, (2012), pp. 22-45*A measure-theoretic computational method for inverse sensitivity problems I: Basic Method and Analysis*, J. Breidt, T. Butler, D. Estep, SIAM Journal on Numerical Analysis, Vol. 49, (2011), pp. 1836-1859*A posteriori error analysis of stochastic differential equations using polynomial chaos expansions*, T. Butler, C. Dawson, T. Wildey, SIAM Journal on Scientific Computing, Vol. 33, (2011), pp. 1267-1291

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### Submitted work (in review/revision) with current status/dates

*Utilizing Response Surface Approximations and Error Estimates to Accurately Predict Probabilities of Events*, T. Butler and T. Wildey, Status: in review since June 2017*A Consistent Bayesian Formulation for Stochastic Inverse Problems Based on Push-forward Measures*, T. Butler, J. Jakeman, and T. Wildey, Status: revised and in review since March 2017

### Papers awaiting submission

*Quantifying Uncertainties in Modeling the Durability of CFRP-Confined Concrete Members Subjected to Sulfuric Acid*Y. Ji, T. Butler, and Y.J. Kim*Solving Stochastic Inverse Problems using Sigma-Algebras on Contour Maps*, T. Butler et. al.*Enhanced surrogate modeling with adjoints for goal-oriented measure-theoretic inversion*, T. Butler and S. Mattis*Simulation-Based Optimal Experimental Design: A Measure-Theoretic Perspective*, T. Butler, M. Pilosov, and S. Walsh