Amersfoort, Joost Van, Lewis Smith, Yee Whye Teh, and Yarin Gal. 2020. “Uncertainty Estimation Using a Single Deep Deterministic Neural Network.”
In International Conference on Machine Learning
, 9690–700. PMLR.
Bhatt, Umang, Javier Antorán, Yunfeng Zhang, Q. Vera Liao, Prasanna Sattigeri, Riccardo Fogliato, Gabrielle Gauthier Melançon, et al. 2021. “Uncertainty as a Form of Transparency: Measuring, Communicating, and Using Uncertainty.” arXiv:2011.07586 [Cs]
Bishop, Christopher. 1994. “Mixture Density Networks.” Microsoft Research
Chipman, Hugh A, Edward I George, and Robert E Mcculloch. 2006. “Bayesian Ensemble Learning.” In, 8.
Daxberger, Erik, Agustinus Kristiadi, Alexander Immer, Runa Eschenhagen, Matthias Bauer, and Philipp Hennig. 2021. “Laplace Redux — Effortless Bayesian Deep Learning.”
In arXiv:2106.14806 [Cs, Stat]
Doherty, John. 2015. Calibration and uncertainty analysis for complex environmental models.
Gal, Yarin, and Zoubin Ghahramani. 2015. “Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning.”
In Proceedings of the 33rd International Conference on Machine Learning (ICML-16)
Ghosh, Soumya, Q. Vera Liao, Karthikeyan Natesan Ramamurthy, Jiri Navratil, Prasanna Sattigeri, Kush R. Varshney, and Yunfeng Zhang. 2021. “Uncertainty Quantification 360: A Holistic Toolkit for Quantifying and Communicating the Uncertainty of AI.” arXiv:2106.01410 [Cs]
Gladish, Daniel W., Daniel E. Pagendam, Luk J. M. Peeters, Petra M. Kuhnert, and Jai Vaze. 2018. “Emulation Engines: Choice and Quantification of Uncertainty for Complex Hydrological Models.” Journal of Agricultural, Biological and Environmental Statistics
23 (1): 39–62.
Higdon, Dave, James Gattiker, Brian Williams, and Maria Rightley. 2008. “Computer Model Calibration Using High-Dimensional Output.” Journal of the American Statistical Association
103 (482): 570–83.
Hooten, Mevin B., William B. Leeds, Jerome Fiechter, and Christopher K. Wikle. 2011. “Assessing First-Order Emulator Inference for Physical Parameters in Nonlinear Mechanistic Models.” Journal of Agricultural, Biological, and Environmental Statistics
16 (4): 475–94.
Jarvenpaa, Marko, Aki Vehtari, and Pekka Marttinen. 2020. “Batch Simulations and Uncertainty Quantification in Gaussian Process Surrogate Approximate Bayesian Computation.”
In Conference on Uncertainty in Artificial Intelligence
, 779–88. PMLR.
Kasim, M. F., D. Watson-Parris, L. Deaconu, S. Oliver, P. Hatfield, D. H. Froula, G. Gregori, et al. 2020. “Up to Two Billion Times Acceleration of Scientific Simulations with Deep Neural Architecture Search.” arXiv:2001.08055 [Physics, Stat]
Kingma, Diederik P., Tim Salimans, and Max Welling. 2015. “Variational Dropout and the Local Reparameterization Trick.”
In Proceedings of the 28th International Conference on Neural Information Processing Systems - Volume 2
, 2575–83. NIPS’15. Cambridge, MA, USA: MIT Press.
Kristiadi, Agustinus, Matthias Hein, and Philipp Hennig. 2021. “Learnable Uncertainty Under Laplace Approximations.”
In Uncertainty in Artificial Intelligence
Lakshminarayanan, Balaji, Alexander Pritzel, and Charles Blundell. 2017. “Simple and Scalable Predictive Uncertainty Estimation Using Deep Ensembles.”
In Proceedings of the 31st International Conference on Neural Information Processing Systems
, 6405–16. NIPS’17. Red Hook, NY, USA: Curran Associates Inc.
Minka, Thomas P. 2001. “Expectation Propagation for Approximate Bayesian Inference.”
In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence
, 362–69. UAI’01. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc.
Mukhoti, Jishnu, Andreas Kirsch, Joost van Amersfoort, Philip H. S. Torr, and Yarin Gal. 2021. “Deterministic Neural Networks with Inductive Biases Capture Epistemic and Aleatoric Uncertainty,”
O’Hagan, Anthony. 2013. “Polynomial Chaos: A Tutorial and Critique from a Statistician’s Perspective,” 20.
Pestourie, Raphaël, Youssef Mroueh, Thanh V. Nguyen, Payel Das, and Steven G. Johnson. 2020. “Active Learning of Deep Surrogates for PDEs: Application to Metasurface Design.” Npj Computational Materials
6 (1): 1–7.
Sacks, Jerome, Susannah B. Schiller, and William J. Welch. 1989. “Designs for Computer Experiments.” Technometrics
31 (1): 41–47.
Sacks, Jerome, William J. Welch, Toby J. Mitchell, and Henry P. Wynn. 1989. “Design and Analysis of Computer Experiments.” Statistical Science
4 (4): 409–23.
Shafer, Glenn, and Vladimir Vovk. 2008. “A Tutorial on Conformal Prediction.” Journal of Machine Learning Research
9 (12): 371–421.
Siade, Adam J., Mario Putti, and William W. G. Yeh. 2010. “Snapshot selection for groundwater model reduction using proper orthogonal decomposition.” Water Resources Research
46 (8): W08539.
Smith, Leonard A. 2000. “Disentangling Uncertainty and Error: On the Predictability of Nonlinear Systems.” In Nonlinear Dynamics and Statistics.
Stuart, Andrew M. 2010. “Inverse Problems: A Bayesian Perspective.” Acta Numerica
Tibshirani, Ryan J, Rina Foygel Barber, Emmanuel Candes, and Aaditya Ramdas. 2019. “Conformal Prediction Under Covariate Shift.”
In Advances in Neural Information Processing Systems
. Vol. 32. Curran Associates, Inc.
Vovk, Vladimir, Alex Gammerman, and Glenn Shafer. 2005. Algorithmic Learning in a Random World. Springer Science & Business Media.
Welter, David E., Jeremy T. White, Randall J. Hunt, and John E. Doherty. 2015. “Approaches in Highly Parameterized Inversion—PEST++ Version 3, a Parameter ESTimation and Uncertainty Analysis Software Suite Optimized for Large Environmental Models.”
USGS Numbered Series 7-C12. Techniques and Methods. Reston, VA: U.S. Geological Survey.
White, Jeremy T., Michael N. Fienen, and John E. Doherty. 2016a. “pyEMU: A Python Framework for Environmental Model Uncertainty Analysis Version .01.”
U.S. Geological Survey.
———. 2016b. “A Python Framework for Environmental Model Uncertainty Analysis.” Environmental Modelling & Software
85 (November): 217–28.
Zeni, Gianluca, Matteo Fontana, and Simone Vantini. 2020. “Conformal Prediction: A Unified Review of Theory and New Challenges.” arXiv:2005.07972 [Cs, Econ, Stat]
Zhang, Dongkun, Lu Lu, Ling Guo, and George Em Karniadakis. 2019. “Quantifying Total Uncertainty in Physics-Informed Neural Networks for Solving Forward and Inverse Stochastic Problems.” Journal of Computational Physics
397 (November): 108850.