A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis. - F. Jay Breidt; Troy D. Butler; Donald J. Estep (SIAM J. Numer. Anal., 2011)

A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions. - Troy D. Butler; Clint Dawson 001; Tim Wildey (SIAM J. Sci. Comput., 2011)

Reparameterization for statistical state estimation applied to differential equations. - Troy D. Butler; Mika Juntunen (J. Comput. Phys., 2012)

A Posteriori Error Analysis of Parameterized Linear Systems Using Spectral Methods. - Troy D. Butler; Paul G. Constantine; Tim Wildey (SIAM J. Matrix Anal. Appl., 2012)

A Computational Measure Theoretic Approach to Inverse Sensitivity Problems II: A Posteriori Error Analysis. - Troy D. Butler; Donald J. Estep; Jeff Sandelin (SIAM J. Numer. Anal., 2012)

Propagation of Uncertainties Using Improved Surrogate Models. - Troy D. Butler; Clint Dawson 001; Tim Wildey (SIAM/ASA J. Uncertain. Quantification, 2013)

A Measure-Theoretic Computational Method for Inverse Sensitivity Problems III: Multiple Quantities of Interest. - Troy D. Butler; Donald J. Estep; Simon Tavener; Clint Dawson 001; Joannes J. Westerink (SIAM/ASA J. Uncertain. Quantification, 2014)

Quantifying uncertainty in material damage from vibrational data. - Troy D. Butler; Antti Huhtala; Mika Juntunen (J. Comput. Phys., 2015)

A Measure-Theoretic Interpretation of Sample Based Numerical Integration with Applications to Inverse and Prediction Problems under Uncertainty. - Troy D. Butler; L. Graham; Steven Mattis; Scot Walsh (SIAM J. Sci. Comput., 2017)

Combining Push-Forward Measures and Bayes' Rule to Construct Consistent Solutions to Stochastic Inverse Problems. - Troy D. Butler; John D. Jakeman; Tim Wildey (SIAM J. Sci. Comput., 2018)

Convergence of Probability Densities Using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification. - Troy D. Butler; John D. Jakeman; Tim Wildey (SIAM J. Sci. Comput., 2018)

Learning Quantities of Interest from Dynamical Systems for Observation-Consistent Inversion. - Steven Mattis; Kyle Robert Steffen; Troy D. Butler; Clint N. Dawson; Donald J. Estep (CoRR, 2020)

Optimal experimental design for prediction based on push-forward probability measures. - Troy D. Butler; John D. Jakeman; Tim Wildey (J. Comput. Phys., 2020)

Parameter Estimation with Maximal Updated Densities. - Michael Pilosov; Carlos del-Castillo-Negrete; Tian Yu Yen; Troy D. Butler; Clint N. Dawson (CoRR, 2022)

A Distributions-Based Approach for Data-Consistent Inversion. - Kirana Bergstrom; Troy D. Butler; Timothy Wildey (SIAM J. Sci. Comput., 2024)

A machine-learning enabled framework for quantifying uncertainties in parameters of computational models. - Taylor Roper; Harri Hakula; Troy D. Butler (Comput. Math. Appl., 2025)