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This paper presents a study using the Bayesian approach in stochastic volatility models for modeling financial time series, using Hamiltonian Monte Carlo methods (HMC). We propose the use of other distributions for the errors in the…

Applications · Statistics 2017-12-07 David S. Dias , Ricardo S. Ehlers

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

Machine Learning · Statistics 2023-02-22 Marvin Schmitt , Stefan T. Radev , Paul-Christian Bürkner

This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…

Methodology · Statistics 2017-07-12 Jon Cockayne , Chris Oates , Tim Sullivan , Mark Girolami

Probabilistic Circuits (PCs) are a promising avenue for probabilistic modeling. They combine advantages of probabilistic graphical models (PGMs) with those of neural networks (NNs). Crucially, however, they are tractable probabilistic…

Machine Learning · Computer Science 2021-06-07 Anji Liu , Guy Van den Broeck

Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…

Computation · Statistics 2014-06-18 José Miguel Pasini , Tuhin Sahai

In the present work, a rate-dependent cohesive zone model for the fracture of polymeric interfaces is presented. Inverse calibration of parameters for such complex models through trial and error is computationally tedious due to the large…

Computational Engineering, Finance, and Science · Computer Science 2023-11-15 Ponkrshnan Thiagarajan , Trisha Sain , Susanta Ghosh

This work investigates Bayesian stepwise estimation (Se) for measuring the two parameters of a unitary qubit rotation. While asymptotic analysis predicts a precision advantage for SE over joint estimation (JE) in regimes where the quantum…

Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both…

Quantum Physics · Physics 2023-11-03 Eric Ghysels , Jack Morgan , Hamed Mohammadbagherpoor

We propose the Variation Calibration Error (VCE) metric for assessing the calibration of machine learning classifiers. The metric can be viewed as an extension of the well-known Expected Calibration Error (ECE) which assesses the…

Machine Learning · Computer Science 2026-02-16 Andrew Thompson , Vivek Desai

The increasing uncertainty level caused by growing renewable energy sources (RES) and aging transmission networks poses a great challenge in the assessment of total transfer capability (TTC) and available transfer capability (ATC). In this…

Signal Processing · Electrical Eng. & Systems 2020-10-29 Xiaoting Wang , Xiaozhe Wang , Hao Sheng , Xi Lin

The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…

Numerical Analysis · Mathematics 2025-06-04 Ruibiao Song , Liying Zhang

In this paper, we study the stochastic collocation (SC) methods for uncertainty quantification (UQ) in hyperbolic systems of nonlinear partial differential equations (PDEs). In these methods, the underlying PDEs are numerically solved at a…

Numerical Analysis · Mathematics 2025-06-19 Alina Chertock , Arsen S. Iskhakov , Safa Janajra , Alexander Kurganov

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a…

Machine Learning · Statistics 2024-11-11 Dimitris G. Giovanis , Dimitrios Loukrezis , Ioannis G. Kevrekidis , Michael D. Shields

Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are…

Dynamical Systems · Mathematics 2018-12-13 Maxime Breden , Christian Kuehn

Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on…

Interactions among multiple time series of positive random variables are crucial in diverse financial applications, from spillover effects to volatility interdependence. A popular model in this setting is the vector Multiplicative Error…

Computation · Statistics 2021-07-12 Nicola Donelli , Stefano Peluso , Antonietta Mira

In this work we focus on the construction of numerical schemes for the approximation of stochastic mean--field equations which preserve the nonnegativity of the solution. The method here developed makes use of a mean-field Monte Carlo…

Numerical Analysis · Mathematics 2018-05-10 J. A. Carrillo , L. Pareschi , M. Zanella

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

In this paper, we consider the so-called Shape Invariant Model which stands for the estimation of a function f0 submitted to a random translation of law g0 in a white noise model. We are interested in such a model when the law of the…

Statistics Theory · Mathematics 2013-03-13 Dominique Bontemps , Sebastien Gadat

Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…

Computational Engineering, Finance, and Science · Computer Science 2022-03-23 Chun Yui Wong , Pranay Seshadri , Andrew B. Duncan , Ashley Scillitoe , Geoffrey Parks