scholarly journals BAYESIAN INFERENCE FOR INVERSE PROBLEMS OCCURRING IN UNCERTAINTY ANALYSIS

2015 ◽  
Vol 5 (1) ◽  
pp. 73-98 ◽  
Author(s):  
Shuai Fu ◽  
Gilles Celeux ◽  
Nicolas Bousquet ◽  
Mathieu Couplet
Keyword(s):  
Bayesian Inference ◽  
Inverse Problems ◽  
Uncertainty Analysis

Inverse Problems With Errors in the Independent Variables Errors-in-Variables, Total Least Squares, and Bayesian Inference

2008 ◽  
Author(s):  
A. F. Emery
Keyword(s):  
Bayesian Inference ◽  
Maximum Likelihood ◽  
Inverse Problems ◽  
Least Squares ◽  
Total Least Squares ◽  
Errors In Variables ◽  
Independent Variables ◽  
Error In Variables ◽  
Best Estimates ◽  
Normally Distributed

Most practioners of inverse problems use least squares or maximum likelihood (MLE) to estimate parameters with the assumption that the errors are normally distributed. When there are errors both in the measured responses and in the independent variables, or in the model itself, more information is needed and these approaches may not lead to the best estimates. A review of the error-in-variables (EIV) models shows that other approaches are necessary and in some cases Bayesian inference is to be preferred.

scholarly journals A Bayesian graph convolutional network for reliable prediction of molecular properties with uncertainty quantification

2019 ◽  
Vol 10 (36) ◽  
pp. 8438-8446 ◽  
Author(s):  
Seongok Ryu ◽  
Yongchan Kwon ◽  
Woo Youn Kim
Keyword(s):  
Neural Networks ◽  
Bayesian Inference ◽  
Uncertainty Analysis ◽  
Uncertainty Quantification ◽  
Deep Neural Networks ◽  
Molecular Properties ◽  
Reliable Prediction ◽  
Convolutional Network ◽  
Chemical Fields

Deep neural networks have been increasingly used in various chemical fields. Here, we show that Bayesian inference enables more reliable prediction with quantitative uncertainty analysis.

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