Colin Fox
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View article: Computational efficient single component Gibbs sampling for electrical tomography
Computational efficient single component Gibbs sampling for electrical tomography Open
Purpose In Bayesian inversion, the Gibbs sampler draws samples from the multivariate posteriori distribution by sequentially sampling from the conditional distributions of the individual parameters. This makes Gibbs sampling a preferable s…
View article: Vectorized finite element matrix assembly and fast Jacobian operations for ATCA systems
Vectorized finite element matrix assembly and fast Jacobian operations for ATCA systems Open
Systems having the form $$A^\text {T}CA$$ appear as governing equations in equilibrium systems, such as the nonlinear inverse problems of EIT, ECT, and ERT (electrical impedance/capacitance/resistance tomography) that motivate our s…
View article: Vibrational Analysis of Building Structures with Irregularities
Vibrational Analysis of Building Structures with Irregularities Open
This paper presents a mathematical model for predicting vibrations in lightweight, timber-based floor/ceiling structures, enhanced to account for irregularities in joist shape and stiffness, as well as floor stiffness. Building on a prior …
View article: Posterior exploration for computationally intensive forward models
Posterior exploration for computationally intensive forward models Open
In this chapter, we address the challenge of exploring the posterior distributions of Bayesian inverse problems with computationally intensive forward models. We consider various multivariate proposal distributions, and compare them with s…
View article: Efficient Jacobian Computations for Complex ECT/EIT Imaging
Efficient Jacobian Computations for Complex ECT/EIT Imaging Open
The reconstruction of the spatial complex conductivity σ+jωε0εr from complex valued impedance measurements forms the inverse problem of complex electrical impedance tomography or complex electrical capacitance tomography. Regularized Gauß-…
View article: Fast numerical techniques for FE simulations in electrical capacitance tomography
Fast numerical techniques for FE simulations in electrical capacitance tomography Open
Purpose Nonlinear solution approaches for inverse problems require fast simulation techniques for the underlying sensing problem. In this work, the authors investigate finite element (FE) based sensor simulations for the inverse problem of…
View article: On the Spatial Response of Electromagnetic Flowmeters
On the Spatial Response of Electromagnetic Flowmeters Open
This paper investigates the spatial response of electromagnetic flowmeters, which are commonly used to measure bulk flow in various industrial applications. While most flowmeters focus on measuring the overall flow rate, this paper explore…
View article: Multilevel Delayed Acceptance MCMC
Multilevel Delayed Acceptance MCMC Open
.We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the multilevel M…
View article: Multilevel Delayed Acceptance MCMC
Multilevel Delayed Acceptance MCMC Open
We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel MC…
View article: Parsimony and the rank of a flattening matrix
Parsimony and the rank of a flattening matrix Open
The standard models of sequence evolution on a tree determine probabilities for every character or site pattern. A flattening is an arrangement of these probabilities into a matrix, with rows corresponding to all possible site patterns for…
View article: V-Spline: An Adaptive Smoothing Spline for Trajectory Reconstruction
V-Spline: An Adaptive Smoothing Spline for Trajectory Reconstruction Open
Trajectory reconstruction is the process of inferring the path of a moving object between successive observations. In this paper, we propose a smoothing spline—which we name the V-spline—that incorporates position and velocity information …
View article: Grid methods for Bayes-optimal continuous-discrete filtering and utilizing a functional tensor train representation
Grid methods for Bayes-optimal continuous-discrete filtering and utilizing a functional tensor train representation Open
Formulae display:?Mathematical formulae have been encoded as MathML and are displayed in this HTML version using MathJax in order to improve their display. Uncheck the box to turn MathJax off. This feature requires Javascript. Click on a f…
View article: Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3
Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3 Open
Uncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when the evaluation it involves solving a Partial Differen…
View article: Randomized Reduced Forward Models for Efficient Metropolis--Hastings\n MCMC, with Application to Subsurface Fluid Flow and Capacitance Tomography
Randomized Reduced Forward Models for Efficient Metropolis--Hastings\n MCMC, with Application to Subsurface Fluid Flow and Capacitance Tomography Open
Bayesian modelling and computational inference by Markov chain Monte Carlo\n(MCMC) is a principled framework for large-scale uncertainty quantification,\nthough is limited in practice by computational cost when implemented in the\nsimplest…
View article: Bayesian Inference of Species Trees using Diffusion Models
Bayesian Inference of Species Trees using Diffusion Models Open
We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics com…
View article: A posteriori stochastic correction of reduced models in delayed‐acceptance MCMC, with application to multiphase subsurface inverse problems
A posteriori stochastic correction of reduced models in delayed‐acceptance MCMC, with application to multiphase subsurface inverse problems Open
Summary Sample‐based Bayesian inference provides a route to uncertainty quantification in the geosciences and inverse problems in general but is very computationally demanding in the naïve form, which requires simulating an accurate comput…
View article: Approximation and sampling of multivariate probability distributions in\n the tensor train decomposition
Approximation and sampling of multivariate probability distributions in\n the tensor train decomposition Open
General multivariate distributions are notoriously expensive to sample from,\nparticularly the high-dimensional posterior distributions in PDE-constrained\ninverse problems. This paper develops a sampler for arbitrary continuous\nmultivari…
View article: Adaptive Approximation Error Models for Efficient Uncertainty Quantification with Application to Multiphase Subsurface Fluid Flow
Adaptive Approximation Error Models for Efficient Uncertainty Quantification with Application to Multiphase Subsurface Fluid Flow Open
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, though is very computationally demanding in the na\ive form that requires simulating an accurate computer model at each iteration. We presen…
View article: A posteriori stochastic correction of reduced models in delayed acceptance MCMC, with application to multiphase subsurface inverse problems
A posteriori stochastic correction of reduced models in delayed acceptance MCMC, with application to multiphase subsurface inverse problems Open
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer mo…
View article: Adaptive Smoothing for Trajectory Reconstruction
Adaptive Smoothing for Trajectory Reconstruction Open
Trajectory reconstruction is the process of inferring the path of a moving object between successive observations. In this paper, we propose a smoothing spline -- which we name the V-spline -- that incorporates position and velocity inform…
View article: Adaptive Smoothing Spline for Trajectory Reconstruction
Adaptive Smoothing Spline for Trajectory Reconstruction Open
Trajectory reconstruction is the process of inferring the path of a moving
\nobject between successive observations. In this paper, we propose a smoothing
\nspline -- which we name the V-spline -- that incorporates position and velocity
\n…
View article: Sampling hyperparameters in hierarchical models: improving on Gibbs for high-dimensional latent fields and large data sets
Sampling hyperparameters in hierarchical models: improving on Gibbs for high-dimensional latent fields and large data sets Open
We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the l…
View article: Sampling hyperparameters in hierarchical models: improving on Gibbs for\n high-dimensional latent fields and large data sets
Sampling hyperparameters in hierarchical models: improving on Gibbs for\n high-dimensional latent fields and large data sets Open
We consider posterior sampling in the very common Bayesian hierarchical model\nin which observed data depends on high-dimensional latent variables that, in\nturn, depend on relatively few hyperparameters. When the full conditional over\nth…
View article: Numerical approximation of the Frobenius-Perron operator using the finite volume method
Numerical approximation of the Frobenius-Perron operator using the finite volume method Open
We develop a finite-dimensional approximation of the Frobenius-Perron operator using the finite volume method applied to the continuity equation for the evolution of probability. A Courant-Friedrichs-Lewy condition ensures that the approxi…
View article: Tuning of MCMC with Langevin, Hamiltonian, and other stochastic autoregressive proposals
Tuning of MCMC with Langevin, Hamiltonian, and other stochastic autoregressive proposals Open
Proposals for Metropolis-Hastings MCMC derived by discretizing Langevin diffusion or Hamiltonian dynamics are examples of stochastic autoregressive proposals that form a natural wider class of proposals with equivalent computability. We an…
View article: Metropolis-Hastings algorithms with autoregressive proposals, and a few examples
Metropolis-Hastings algorithms with autoregressive proposals, and a few examples Open
We analyse computational efficiency of Metropolis-Hastings algorithms with stochastic AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g. HM…