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This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the…

Methodology · Statistics 2024-07-30 Zhao Mingyang , Jia Xiaohong , Ma Lei , Shi Yuke , Jiang Jingen , Li Qizhai , Yan Dong-Ming , Huang Tiejun

We investigate the inverse problem of determining nonlinear elastic material parameters from boundary stress measurements corresponding to prescribed boundary displacements. The material law is described by a nonlinear, space-independent…

Analysis of PDEs · Mathematics 2026-01-23 David Johansson , Yavar Kian

We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to…

Statistics Theory · Mathematics 2023-11-07 Duc-Lam Duong , Tapio Helin , Jose Rodrigo Rojo-Garcia

Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal…

Computation · Statistics 2018-03-14 David J. Price , Nigel G. Bean , Joshua V. Ross , Jonathan Tuke

Traditionally Bayesian decision-theoretic design of experiments proceeds by choosing a design to minimise expectation of a given loss function over the space of all designs. The loss function encapsulates the aim of the experiment, and the…

Methodology · Statistics 2021-08-10 Antony M. Overstall , James M. McGree

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

Statistics Theory · Mathematics 2021-02-23 Junxiong Jia , Jigen Peng , Jinghuai Gao

A Bayesian design is given by maximising an expected utility over a design space. The utility is chosen to represent the aim of the experiment and its expectation is taken with respect to all unknowns: responses, parameters and/or models.…

Methodology · Statistics 2019-01-16 Antony M. Overstall , James M. McGree

In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…

Computation · Statistics 2022-06-08 Max Ehre , Rafael Flock , Martin Fußeder , Iason Papaioannou , Daniel Straub

We consider Bayesian linear inverse problems in infinite-dimensional separable Hilbert spaces, with a Gaussian prior measure and additive Gaussian noise model, and provide an extension of the concept of Bayesian D-optimality to the…

Statistics Theory · Mathematics 2014-09-04 Alen Alexanderian , Philip Gloor , Omar Ghattas

Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible,…

Machine Learning · Statistics 2019-02-26 Steven Kleinegesse , Michael Gutmann

We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems for which the observational map is based on partial differential equations and, consequently, is computationally expensive to evaluate.…

Numerical Analysis · Mathematics 2023-08-14 Vinh Hoang , Luis Espath , Sebastian Krumscheid , Raúl Tempone

We propose a Bayesian framework for feedback boundary control for hyperbolic balance laws. The method propagates a probability distribution over feedback parameters by using Lyapunov decay estimates as a likelihood. In the linear setting,…

Numerical Analysis · Mathematics 2026-02-03 Markus Bambach , Shaoshuai Chu , Michael Herty , Yunong Lin

Doubly-intractable posterior distributions arise in many applications of statistics concerned with discrete and dependent data, including physics, spatial statistics, machine learning, the social sciences, and other fields. A specific…

Computation · Statistics 2021-05-20 Jaewoo Park , Ick Hoon Jin , Michael Schweinberger

The construction of decision-theoretic Bayesian designs for realistically-complex nonlinear models is computationally challenging, as it requires the optimization of analytically intractable expected utility functions over high-dimensional…

Methodology · Statistics 2016-07-01 Antony Overstall , David Woods

The reconstruction of the structure of biological tissue using electromyographic data is a non-invasive imaging method with diverse medical applications. Mathematically, this process is an inverse problem. Furthermore, electromyographic…

Numerical Analysis · Mathematics 2021-05-26 Anna Rörich , Tim A. Werthmann , Dominik Göddeke , Lars Grasedyck

Bayesian experimental design is a technique that allows to efficiently select measurements to characterize a physical system by maximizing the expected information gain. Recent developments in deep neural networks and normalizing flows…

Quantum Physics · Physics 2023-06-27 Leopoldo Sarra , Florian Marquardt

Systems with both quantitative and qualitative responses are widely encountered in many applications. Design of experiment methods are needed when experiments are conducted to study such systems. Classic experimental design methods are…

Methodology · Statistics 2023-04-24 Lulu Kang , Xinwei Deng , Ran Jin

This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…

Medical Physics · Physics 2009-10-31 R. Hasson , S. J. Swithenby

We present an analytical model to investigate the mechanics of 2-dimensional lattices composed of elastic beams of non-uniform cross-section. Our approach is based on reducing a lattice to a single beam subject to the action of a set of…

Soft Condensed Matter · Physics 2016-02-22 Daniel J. Rayneau-Kirkhope , Marcelo A. Dias

We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…

Statistics Theory · Mathematics 2018-09-05 Mathias Trabs