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Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…

Data Analysis, Statistics and Probability · Physics 2013-01-31 Andreas Raue , Clemens Kreutz , Fabian Joachim Theis , Jens Timmer

This report addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state…

Statistics Theory · Mathematics 2018-10-26 Jean-Baptiste Durand , Y. Guédon

The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators allows for formal statistical quantification of the error due to discretisation in the numerical context. Competing…

Methodology · Statistics 2018-05-23 Junyang Wang , Jon Cockayne , Chris Oates

Addressing uncertainty is critical for autonomous systems to robustly adapt to the real world. We formulate the problem of model uncertainty as a continuous Bayes-Adaptive Markov Decision Process (BAMDP), where an agent maintains a…

Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…

Methodology · Statistics 2023-09-04 Takuo Matsubara , Jeremias Knoblauch , François-Xavier Briol , Chris. J. Oates

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Machine Learning · Statistics 2020-02-27 Tim Pearce , Felix Leibfried , Alexandra Brintrup , Mohamed Zaki , Andy Neely

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

Machine Learning · Computer Science 2019-04-03 Konstantin Posch , Jürgen Pilz

We address the challenge of quantifying Bayesian uncertainty and incorporating it in offline use cases of finite-state Markov Decision Processes (MDPs) with unknown dynamics. Our approach provides a principled method to disentangle…

Machine Learning · Computer Science 2024-06-05 Filippo Valdettaro , A. Aldo Faisal

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…

Logic in Computer Science · Computer Science 2018-06-12 Dimitrios Milios , Guido Sanguinetti , David Schnoerr

Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the…

Numerical Analysis · Mathematics 2025-10-09 Joseph Hart , Bart van Bloemen Waanders , Jixian Li , Timbwaoga A. J. Ouermi , Chris R. Johnson

Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…

Methodology · Statistics 2025-05-26 Clara Grazian

In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…

Methodology · Statistics 2023-04-28 Konstantinos E. Tatsis , Vasilis K. Dertimanis , Eleni N. Chatzi

The construction and formal verification of dynamical models is important in engineering, biology and other disciplines. We focus on non-linear models containing a set of parameters governing their dynamics. The value of these parameters is…

Systems and Control · Computer Science 2015-04-20 Benjamin M. Gyori , Daniel Paulin , Sucheendra K. Palaniappan

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

Machine Learning · Statistics 2019-05-28 Aliaksandr Hubin , Geir Storvik

Survival models are used in various fields, such as the development of cancer treatment protocols. Although many statistical and machine learning models have been proposed to achieve accurate survival predictions, little attention has been…

Machine Learning · Computer Science 2020-03-26 Hrushikesh Loya , Pranav Poduval , Deepak Anand , Neeraj Kumar , Amit Sethi

Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations…

Machine Learning · Computer Science 2024-05-08 Yongquan Qu , Mohamed Aziz Bhouri , Pierre Gentine

Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps.…

Machine Learning · Computer Science 2020-11-25 Cheng Wang , Carolin Lawrence , Mathias Niepert

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

Methodology · Statistics 2024-07-02 Isadora Antoniano-Villalobos , Emanuele Borgonovo , Xuefei Lu

In this paper we address the problem of discretization in the context of learning Bayesian networks (BNs) from data containing both continuous and discrete variables. We describe a new technique for <EM>multivariate</EM> discretization,…

Artificial Intelligence · Computer Science 2013-02-01 Stefano Monti , Gregory F. Cooper

Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…

Dynamical Systems · Mathematics 2008-11-25 Jinqiao Duan