A unified framework for multilevel uncertainty quantification in Bayesian inverse problems
نویسندگان
چکیده
منابع مشابه
An Efficient MCMC Method for Uncertainty Quantification in Inverse Problems
The connection between Bayesian statistics and the technique of regularization for inverse problems has been given significant attention in recent years. For example, Bayes’ law is frequently used as motivation for variational regularization methods of Tikhonov type. In this setting, the regularization function corresponds to the negative-log of the prior probability density; the fit-to-data fu...
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 کاملData Analysis Tools for Uncertainty Quantification of Inverse Problems
We present exploratory data analysis methods to assess inversion estimates using examples based on �2and �1-regularization. These methods can be used to reveal the presence of systematic errors such as bias and discretization effects, or to validate assumptions made on the statistical model used in the analysis. The methods include: bounds on the performance of randomized estimators of a large ...
متن کاملUnified Framework for Quantification
Quantification is the machine learning task of estimating test-data class proportions that are not necessarily similar to those in training. Apart from its intrinsic value as an aggregate statistic, quantification output can also be used to optimize classifier probabilities, thereby increasing classification accuracy. We unify major quantification approaches under a constrained multi-variate re...
متن کاملA Bayesian multiscale framework for Poisson inverse problems
This paper describes a maximum a postetioti (MAP) estimation method for linear inverse problems involving Poisson data based on a novel multiscale framework. The framework itself is founded on a carefully designed multiscale prior probability distribution placed on the “splits” in the multiscale partition of the underlying intensity, and it admits a remarkably simple MAP estimation procedure us...
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: Probabilistic Engineering Mechanics
سال: 2016
ISSN: 0266-8920
DOI: 10.1016/j.probengmech.2015.09.007