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Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

Dynamical Systems · Mathematics 2024-03-25 Anna Fitzpatrick , Molly Folino , Andrea Arnold

Ensemble forecasts of weather and climate are subject to systematic biases in the ensemble mean and variance, leading to inaccurate estimates of the forecast mean and variance. To address these biases, ensemble forecasts are post-processed…

Applications · Statistics 2016-05-25 Stefan Siegert , Philip G. Sansom , Robin Williams

The ability to identify and resolve uncertainty is crucial for the robustness of a dialogue system. Indeed, this has been confirmed empirically on systems that utilise Bayesian approaches to dialogue belief tracking. However, such systems…

Computation and Language · Computer Science 2021-09-10 Carel van Niekerk , Andrey Malinin , Christian Geishauser , Michael Heck , Hsien-chin Lin , Nurul Lubis , Shutong Feng , Milica Gašić

Detecting abrupt changes in the mean of a time series, so-called changepoints, is important for many applications. However, many procedures rely on the estimation of nuisance parameters (like long-run variance). Under the alternative (a…

Statistics Theory · Mathematics 2018-08-14 Michal Pešta , Martin Wendler

The opaque nature of transformer-based models, particularly in applications susceptible to unethical practices such as dark-patterns in user interfaces, requires models that integrate uncertainty quantification to enhance trust in…

Machine Learning · Computer Science 2024-12-09 Javier Muñoz , Álvaro Huertas-García , Carlos Martí-González , Enrique De Miguel Ambite

Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for…

Computer Vision and Pattern Recognition · Computer Science 2026-02-19 M. M. A. Valiuddin , R. J. G. van Sloun , C. G. A. Viviers , P. H. N. de With , F. van der Sommen

We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available…

Machine Learning · Computer Science 2020-03-19 Yongxin Chen , Tryphon T. Georgiou , Allen R. Tannenbaum

In many settings, such as scientific inference, optimization, and transfer learning, the learner has a well-defined objective, which can be treated as estimation of a target parameter, and no intrinsic interest in characterizing the entire…

Machine Learning · Computer Science 2025-07-23 Sabina J. Sloman , Ayush Bharti , Julien Martinelli , Samuel Kaski

We introduce a framework for uncertainty estimation that both describes and extends many existing methods. We consider typical hyperparameters involved in classical training as random variables and marginalise them out to capture various…

Machine Learning · Computer Science 2021-07-07 Francesco Farina , Lawrence Phillips , Nicola J Richmond

We seek to conduct statistical inference for a large collection of primary parameters, each with its own nuisance parameters. Our approach is partially Bayesian, in that we treat the primary parameters as fixed while we model the nuisance…

Methodology · Statistics 2025-12-10 Nikolaos Ignatiadis , Li Ma

When conducting inference for the average treatment effect on the treated with a Synthetic Control Estimator, the vector of control weights is a nuisance parameter which is often constrained, high-dimensional, and may be only partially…

Econometrics · Economics 2025-07-03 Joseph Fry

Statistical models typically capture uncertainties in our knowledge of the corresponding real-world processes, however, it is less common for this uncertainty specification to capture uncertainty surrounding the values of the inputs to the…

Methodology · Statistics 2023-05-10 Samuel E. Jackson , David C. Woods

Artificial neural networks will always make a prediction, even when completely uncertain and regardless of the consequences. This obliviousness of uncertainty is a major obstacle towards their adoption in practice. Techniques exist,…

Machine Learning · Computer Science 2021-05-13 Hans Weytjens , Jochen De Weerdt

Gaussian Process (GP) models have also become extremely useful for optimization under uncertainty algorithms, especially where the objective functions are costly to compute. Yet, the more classical methods usually adopt strategies that, in…

Optimization and Control · Mathematics 2025-07-22 Nishant Gadde

This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a…

Statistics Theory · Mathematics 2014-09-24 Isaiah Andrews , Anna Mikusheva

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

Machine Learning · Statistics 2019-03-11 Konstantin Posch , Jan Steinbrener , Jürgen Pilz

We present a method to quantify uncertainty in the predictions made by simulations of mathematical models that can be applied to a broad class of stochastic, discrete, and differential equation models. Quantifying uncertainty is crucial for…

Machine Learning · Statistics 2015-03-05 Kyle S. Hickmann , James M. Hyman , Sara Y. Del Valle

Single-channel deep speech enhancement approaches often estimate a single multiplicative mask to extract clean speech without a measure of its accuracy. Instead, in this work, we propose to quantify the uncertainty associated with clean…

Audio and Speech Processing · Electrical Eng. & Systems 2023-05-16 Huajian Fang , Timo Gerkmann

Weak identification arises in many statistical problems when key variables exhibit weak correlations-for example, when instrumental variables correlate weakly with treatment, or when proxy variables correlate weakly with unmeasured…

Statistics Theory · Mathematics 2025-11-12 Rui Wang , Kwun Chuen Gary Chan , Ting Ye

Time series models are ubiquitous in science, arising in any situation where researchers seek to understand how a system's behaviour changes over time. A key problem in time series modelling is \emph{inference}; determining properties of…

Mathematical Software · Computer Science 2020-01-13 Michael Clerx , Martin Robinson , Ben Lambert , Chon Lok Lei , Sanmitra Ghosh , Gary R. Mirams , David J. Gavaghan