scholarly journals On the equivalence between total least squares and maximum likelihood PCA

2005 ◽  
Vol 544 (1-2) ◽  
pp. 254-267 ◽  
Author(s):  
M. Schuermans ◽  
I. Markovsky ◽  
Peter D. Wentzell ◽  
S. Van Huffel
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Total Least Squares

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.

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