Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
نویسندگان
چکیده
منابع مشابه
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a spatial or temporal field, endowed with a hierarchical Gaussian process prior. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of Markov chain Monte Carlo) and are compounded by high dimensionality of the posterior...
متن کاملLimitations of polynomial chaos expansions in the Bayesian solution of inverse problems
Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting esti...
متن کاملBayesian Inference Tools for Inverse Problems
In this paper, first the basics of the Bayesian inference for linear inverse problems are presented. The inverse problems we consider are, for example, signal deconvolution, image restoration or image reconstruction in Computed Tomography (CT). The main point to discuss then is the prior modeling of signals and images. We consider two classes of priors: simple or hierarchical with hidden variab...
متن کاملBayesian Inference for Inverse Problems Occurring in Uncertainty Analysis
The inverse problem considered here is the estimation of the distribution of a nonobserved random variable X , linked through a time-consuming physical model H to some noisy observed data Y . Bayesian inference is considered to account for prior expert knowledge on X in a small sample size setting. A Metropolis-Hastings-within-Gibbs algorithm is used to compute the posterior distribution of the...
متن کاملA Stochastic Collocation Approach to Bayesian Inference in Inverse Problems
We present an efficient numerical strategy for the Bayesian solution of inverse problems. Stochastic collocation methods, based on generalized polynomial chaos (gPC), are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. This approximation then defines a surrogate posterior probability density that can be evaluated repeatedly at min...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2009
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2008.11.024