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AuthorTempone, Raul (10)Scavino, Marco (5)Sawlan, Zaid A (4)Ruggeri, Fabrizio (3)Babuska, Ivo (2)View MoreDepartment

Applied Mathematics and Computational Science Program (11)

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (11)

Statistics Program (1)Subject
Bayesian (11)

View MoreTypePoster (11)Year (Issue Date)2016 (8)2014 (3)Item AvailabilityOpen Access (11)

Now showing items 1-10 of 11

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Bayesian inference and model comparison for metallic fatigue data

Babuska, Ivo; Sawlan, Zaid A; Scavino, Marco; Szabó, Barma; Tempone, Raul (2016-01-06) [Poster]

In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. We then compare and rank the models by classical measures of fit based on information criteria. We also consider a Bayesian approach that provides, under the prior distribution of the model parameters selected by the user, their simulation-based posterior distributions.

Multilevel ensemble Kalman filter

Chernov, Alexey; Hoel, Haakon; Law, Kody; Nobile, Fabio; Tempone, Raul (2016-01-06) [Poster]

This work embeds a multilevel Monte Carlo (MLMC) sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF). In terms of computational cost vs. approximation error the asymptotic performance of the multilevel ensemble Kalman filter (MLEnKF) is superior to the EnKF s.

Fast Bayesian Optimal Experimental Design for Seismic Source Inversion

Long, Quan; Motamed, Mohammad; Tempone, Raul (2016-01-06) [Poster]

We develop a fast method for optimally designing experiments [1] in the context of statistical seismic source inversion [2]. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by the elastic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the true parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.

Bayesian inference of the heat transfer properties of a wall using experimental data

Iglesias, Marco; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul; Wood, Christopher (2016-01-06) [Poster]

A hierarchical Bayesian inference method is developed to estimate the thermal resistance and volumetric heat capacity of a wall. We apply our methodology to a real case study where measurements are recorded each minute from two temperature probes and two heat flux sensors placed on both sides of a solid brick wall along a period of almost five days. We model the heat transfer through the wall by means of the one-dimensional heat equation with Dirichlet boundary conditions.
The initial/boundary conditions for the temperature are approximated by piecewise linear functions. We assume that temperature and heat flux measurements have independent Gaussian noise and derive the joint likelihood of the wall parameters and the initial/boundary conditions. Under the model assumptions, the boundary conditions are marginalized analytically from the joint likelihood. ApproximatedGaussian posterior distributions for the wall parameters and the initial condition parameter are obtained using the Laplace method, after incorporating the available prior information. The information gain is estimated under different experimental setups, to determine the best allocation of resources.

Multiscale Modeling of Wear Degradation

Moraes, Alvaro; Ruggeri, Fabrizio; Tempone, Raul; Vilanova, Pedro (2016-01-06) [Poster]

Cylinder liners of diesel engines used for marine propulsion are naturally subjected to a wear process, and may fail when their wear exceeds a specified limit. Since failures often represent high economical costs, it is utterly important to predict and avoid them. In this work [4], we model the wear process using a pure jump process. Therefore, the inference goal here is to estimate: the number of possible jumps, its sizes, the coefficients and the shapes of the jump intensities. We propose a multiscale approach for the inference problem that can be seen as an indirect inference scheme. We found that using a Gaussian approximation based on moment expansions, it is possible to accurately estimate the jump intensities and the jump amplitudes. We obtained results equivalent to the state of the art but using a simpler and less expensive approach.

An Efficient Forward-Reverse EM Algorithm for Statistical Inference in Stochastic Reaction Networks

Bayer, Christian; Moraes, Alvaro; Tempone, Raul; Vilanova, Pedro (2016-01-06) [Poster]

In this work [1], we present an extension of the forward-reverse algorithm by Bayer and Schoenmakers [2] to the context of stochastic reaction networks (SRNs). We then apply this bridge-generation technique to the statistical inference problem of approximating the reaction coefficients based on discretely observed data. To this end, we introduce an efficient two-phase algorithm in which the first phase is deterministic and it is intended to provide a starting point for the second phase which is the Monte Carlo EM Algorithm.

Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

Ruggeri, Fabrizio; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul (2016-01-06) [Poster]

In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

Hierarchical matrix approximation of large covariance matrices

Litvinenko, Alexander; Genton, Marc G.; Sun, Ying (2016-01-06) [Poster]

Fast Estimation of Expected Information Gain for Bayesian Experimental Design Based on Laplace Approximation

Long, Quan; Scavino, Marco; Tempone, Raul; Wang, Suojin (2014-01-06) [Poster]

Shannon-type expected information gain is an important utility in evaluating the usefulness of a proposed experiment that involves uncertainty. Its estimation, however, cannot rely solely on Monte Carlo sampling methods, that are generally too computationally expensive for realistic physical models, especially for those involving the solution of stochastic partial differential equations. In this work we present a new methodology, based on the Laplace approximation of the posterior probability density function, to accelerate the estimation of expected information gain in the model parameters and predictive quantities of interest. Furthermore, in order to deal with the issue of dimensionality in a complex problem, we use sparse quadratures for the integration over the prior. We show the accuracy and efficiency of the proposed method via several nonlinear numerical examples, including a single parameter design of one dimensional cubic polynomial function and the current pattern for impedance tomography.

A Bayesian setting for an inverse problem in heat transfer

Ruggeri, Fabrizio; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul (2014-01-06) [Poster]

In this work a Bayesian setting is developed to infer the thermal conductivity, an unknown parameter that appears into heat equation. Temperature data are available on the basis of cooling experiments. The realistic assumption that the boundary data are noisy is introduced, for a given prescribed initial condition. We show how to derive the global likelihood function for the forward boundary-initial condition problem, given the values of the temperature field plus Gaussian noise. We assume that the thermal conductivity parameter can be modelled a priori through a lognormal distributed random variable or by means of a space-dependent stationary lognormal random field. In both cases, given Gaussian priors for the time-dependent Dirichlet boundary values, we marginalize out analytically the joint posterior distribution of and the random boundary conditions, TL and TR, using the linearity of the heat equation. Synthetic data are used to carry out the inference. We exploit the concentration of the posterior distribution of , using the Laplace approximation and therefore avoiding costly MCMC computations.

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