118 results found
Roininen L, Girolami M, Lasanen S, et al., 2019, HYPERPRIORS FOR MATERN FIELDS WITH APPLICATIONS IN BAYESIAN INVERSION, INVERSE PROBLEMS AND IMAGING, Vol: 13, Pages: 1-29, ISSN: 1930-8337
Briol F-X, Oates CJ, Girolami M, et al., Rejoinder for "Probabilistic Integration: A Role in Statistical Computation?"
This article is the rejoinder for the paper "Probabilistic Integration: ARole in Statistical Computation?" to appear in Statistical Science withdiscussion. We would first like to thank the reviewers and many of ourcolleagues who helped shape this paper, the editor for selecting our paper fordiscussion, and of course all of the discussants for their thoughtful,insightful and constructive comments. In this rejoinder, we respond to some ofthe points raised by the discussants and comment further on the fundamentalquestions underlying the paper: (i) Should Bayesian ideas be used in numericalanalysis?, and (ii) If so, what role should such approaches have in statisticalcomputation?
Briol F-X, Oates CJ, Girolami M, et al., Probabilistic Integration: A Role in Statistical Computation?
A research frontier has emerged in scientific computation, wherein numericalerror is regarded as a source of epistemic uncertainty that can be modelled.This raises several statistical challenges, including the design of statisticalmethods that enable the coherent propagation of probabilities through a(possibly deterministic) computational work-flow. This paper examines the casefor probabilistic numerical methods in routine statistical computation. Ourfocus is on numerical integration, where a probabilistic integrator is equippedwith a full distribution over its output that reflects the presence of anunknown numerical error. Our main technical contribution is to establish, forthe first time, rates of posterior contraction for these methods. These showthat probabilistic integrators can in principle enjoy the "best of bothworlds", leveraging the sampling efficiency of Monte Carlo methods whilstproviding a principled route to assess the impact of numerical error onscientific conclusions. Several substantial applications are provided forillustration and critical evaluation, including examples from statisticalmodelling, computer graphics and a computer model for an oil reservoir.
Lau FD-H, Adams NM, Girolami MA, et al., 2018, The role of statistics in data-centric engineering, STATISTICS & PROBABILITY LETTERS, Vol: 136, Pages: 58-62, ISSN: 0167-7152
Mac Aodha O, Gibb R, Barlow KE, et al., 2018, Bat detective-Deep learning tools for bat acoustic signal detection, PLOS COMPUTATIONAL BIOLOGY, Vol: 14, ISSN: 1553-734X
Lau D, Butler L, Adams N, et al., Real-time Statistical Modelling of Data Generated from Self-Sensing Bridges, Proceedings of the Institution of Civil Engineers - Civil Engineering, ISSN: 0965-089X
Stathopoulos V, Zamora-Gutierrez V, Jones KE, et al., 2018, Bat echolocation call identification for biodiversity monitoring: a probabilistic approach, JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS, Vol: 67, Pages: 165-183, ISSN: 0035-9254
Dunlop MM, Girolami MA, Stuart AM, et al., 2018, How Deep Are Deep Gaussian Processes?, JOURNAL OF MACHINE LEARNING RESEARCH, Vol: 19, ISSN: 1532-4435
Mendoza A, Roininen L, Girolami M, et al., 2018, Statistical methods to enable practical on-site tomographic imaging of whole-core samples
Copyright 2018, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors. We show that statistical methods enable the use of portable industrial scanners (with sparse measurements), suitable for fast on-site whole-core X-ray computerized tomography (CT), as opposed to conventional (medical) devices (with dense measurements). This approach accelerates an informed first-stage general assessment of core samples. To that end, we show that this novel industrial tomographic measurement principle is feasible for rock sample imaging, in conjunction with suitable forms of priors in Bayesian inversion algorithms. We assess the performance of the inversion with Gaussian, Cauchy, and Total Variation (TV) priors. In so doing, we consider, in discrete form, conditional mean (CM) estimators, via Markov Chain Monte Carlo (MCMC) algorithms with noise-contaminated measurements. To benchmark the reliability of whole-core imaging with sparse radiograms via Bayesian inversion, in our study we include X-ray CT from numerical simulations of synthetic and measurement-based whole-core samples. To that end, we consider tomographic measurements of fine- to medium-grained sandstone core samples, with igneous-rich pebbles from the Miocene, off the Shimokita Peninsula in Japan, and fractured welded tuff from Big Bend National Park, Texas. Bayesian inversion results show that with only 16 radiograms, natural fractures with aperture of less than 2mm wide are detectable. Additionally, images show approximately spherical concretions of 6mm diameter. We show that to achieve similar results, filtered back projection (FBP) techniques require hundreds of radiograms, only possible with conventional (medical) laboratory scanners. This paper shows that Bayesian inversion on whole-core X-ray CT is capable of imaging coarse sedimentary features that, with faster, simplified measurement principles, would aid in more efficient operational petrophysical decisions f
Xi X, Briol FX, Girolami M, 2018, Bayesian quadrature for multiple related integrals, Pages: 8533-8564
© 35th International Conference on Machine Learning, ICML 2018.All Rights Reserved. Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to incomplete/finite information about the continuous mathematical problem being approximated. In this paper, we demonstrate that this paradigm can provide additional advantages, such as the possibility of transferring information between several numerical methods. This allows users to represent uncertainty in a more faithful manner and, as a by-product, provide increased numerical efficiency. We propose the first such numerical method by extending the well-known Bayesian quadrature algorithm to the case where we are interested in computing the integral of several related functions. We then prove convergence rates for the method in the well-specified and misspecified cases, and demonstrate its efficiency in the context of multi-fidelity models for complex engineering systems and a problem of global illumination in computer graphics.
Barp A, Briol F-X, Kennedy AD, et al., 2018, Geometry and Dynamics for Markov Chain Monte Carlo, ANNUAL REVIEW OF STATISTICS AND ITS APPLICATION, VOL 5, Vol: 5, Pages: 451-471, ISSN: 2326-8298
Noonan J, Asiala SM, Grassia G, et al., 2018, In vivo multiplex molecular imaging of vascular inflammation using surface-enhanced Raman spectroscopy, THERANOSTICS, Vol: 8, Pages: 6195-6209, ISSN: 1838-7640
Betancourt M, Byrne S, Livingstone S, et al., 2017, The geometric foundations of Hamiltonian Monte Carlo, BERNOULLI, Vol: 23, Pages: 2257-2298, ISSN: 1350-7265
Conrad PR, Girolami M, Sarkka S, et al., 2017, Statistical analysis of differential equations: introducing probability measures on numerical solutions, STATISTICS AND COMPUTING, Vol: 27, Pages: 1065-1082, ISSN: 0960-3174
Oates CJ, Girolami M, Chopin N, 2017, Control functionals for Monte Carlo integration, JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, Vol: 79, Pages: 695-718, ISSN: 1369-7412
Beskos A, Girolami M, Lan S, et al., 2017, Geometric MCMC for infinite-dimensional inverse problems, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 335, Pages: 327-351, ISSN: 0021-9991
Jensen K, Soguero-Ruiz C, Mikalsen KO, et al., 2017, Analysis of free text in electronic health records for identification of cancer patient trajectories, SCIENTIFIC REPORTS, Vol: 7, ISSN: 2045-2322
Cockayne J, Oates C, Sullivan T, et al., 2017, Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems, 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt), Publisher: AMER INST PHYSICS, ISSN: 0094-243X
, 2017, Probabilistic models for integration error in the assessment of functional cardiac models, Pages: 110-118, ISSN: 1049-5258
© 2017 Neural information processing systems foundation. All rights reserved. This paper studies the numerical computation of integrals, representing estimates or predictions, over the output f(x) of a computational model with respect to a distribution p(dx) over uncertain inputs x to the model. For the functional cardiac models that motivate this work, neither f nor p possess a closed-form expression and evaluation of either requires ≈ 100 CPU hours, precluding standard numerical integration methods. Our proposal is to treat integration as an estimation problem, with a joint model for both the a priori unknown function f and the a priori unknown distribution p. The result is a posterior distribution over the integral that explicitly accounts for dual sources of numerical approximation error due to a severely limited computational budget. This construction is applied to account, in a statistically principled manner, for the impact of numerical errors that (at present) are confounding factors in functional cardiac model assessment.
Ellam L, Strathmann H, Girolami M, et al., 2017, A determinant-free method to simulate the parameters of large Gaussian fields, STAT, Vol: 6, Pages: 271-281, ISSN: 2049-1573
, 2017, On the sampling problem for Kernel quadrature, Pages: 949-968
© 2017 by the author(s). The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio s/d, where s and d encode the smoothness and dimension of the integrand. However, an empirical investigation reveals that the rate constant C is highly sensitive to the distribution of the random points. In contrast to standard Monte Carlo integration, for which optimal importance sampling is well-understood, the sampling distribution that minimises C for Kernel Quadrature does not admit a closed form. This paper argues that the practical choice of sampling distribution is an important open problem. One solution is considered; a novel automatic approach based on adaptive tempering and sequential Monte Carlo. Empirical results demonstrate a dramatic reduction in integration error of up to 4 orders of magnitude can be achieved with the proposed method.
Oates CJ, Niederer S, Lee A, et al., 2017, Probabilistic Models for Integration Error in the Assessment of Functional Cardiac Models, 31st Conference on Neural Information Processing Systems (NIPS), Publisher: NEURAL INFORMATION PROCESSING SYSTEMS (NIPS), ISSN: 1049-5258
Chkrebtii OA, Campbell DA, Calderhead B, et al., 2016, Bayesian Solution Uncertainty Quantification for Differential Equations, BAYESIAN ANALYSIS, Vol: 11, Pages: 1239-1267, ISSN: 1931-6690
, 2016, A Bayesian approach to multiscale inverse problems with on-the-fly scale determination, Journal of Computational Physics, Vol: 326, Pages: 115-140, ISSN: 0021-9991
© 2016 Elsevier Inc. A Bayesian computational approach is presented to provide a multi-resolution estimate of an unknown spatially varying parameter from indirect measurement data. In particular, we are interested in spatially varying parameters with multiscale characteristics. In our work, we consider the challenge of not knowing the characteristic length scale(s) of the unknown a priori, and present an algorithm for on-the-fly scale determination. Our approach is based on representing the spatial field with a wavelet expansion. Wavelet basis functions are hierarchically structured, localized in both spatial and frequency domains and tend to provide sparse representations in that a large number of wavelet coefficients are approximately zero. For these reasons, wavelet bases are suitable for representing permeability fields with non-trivial correlation structures. Moreover, the intra-scale correlations between wavelet coefficients form a quadtree, and this structure is exploited to identify additional basis functions to refine the model. Bayesian inference is performed using a sequential Monte Carlo (SMC) sampler with a Markov Chain Monte Carlo (MCMC) transition kernel. The SMC sampler is used to move between posterior densities defined on different scales, thereby providing a computationally efficient method for adaptive refinement of the wavelet representation. We gain insight from the marginal likelihoods, by computing Bayes factors, for model comparison and model selection. The marginal likelihoods provide a termination criterion for our scale determination algorithm. The Bayesian computational approach is rather general and applicable to several inverse problems concerning the estimation of a spatially varying parameter. The approach is demonstrated with permeability estimation for groundwater flow using pressure sensor measurements.
House T, Ford A, Lan S, et al., 2016, Bayesian uncertainty quantification for transmissibility of influenza, norovirus and Ebola using information geometry, JOURNAL OF THE ROYAL SOCIETY INTERFACE, Vol: 13, ISSN: 1742-5689
Oates CJ, Papamarkou T, Girolami M, 2016, The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation, JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, Vol: 111, Pages: 634-645, ISSN: 0162-1459
Lan S, Bui-Thanh T, Christie M, et al., 2016, Emulation of higher-order tensors in manifold Monte Carlo methods for Bayesian Inverse Problems, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 308, Pages: 81-101, ISSN: 0021-9991
Gracie K, Moores M, Smith WE, et al., 2016, Preferential Attachment of Specific Fluorescent Dyes and Dye Labeled DNA Sequences in a Surface Enhanced Raman. Scattering Multiplex, ANALYTICAL CHEMISTRY, Vol: 88, Pages: 1147-1153, ISSN: 0003-2700
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