Iterative least-squares solver for generalized maximum-likelihood ptychography

Least squares and maximum likelihood

Least squares methods in maximum likelihood problems

It is well known that the GaussNewton algorithm for solving nonlinear least squares problems is a special case of the scoring algorithm for maximizing log likelihoods. What has received less attention is that the computation of the current correction in the scoring algorithm in both its line search and trust region forms can be cast as a linear least squares problem. This is an important observ...

Maximum Likelihood Recursive Least Squares Estimation for Multivariable Systems

This paper discusses parameter estimation problems of the multivariable systems described by input–output difference equations. We decompose a multivariable system to several subsystems according to the number of the outputs. Based on the maximum likelihood principle, a maximum likelihood-based recursive least squares algorithm is derived to estimate the parameters of each subsystem. Finally, t...

Estimation by Least Squares and by Maximum Likelihood

Although statements to the contrary are often made, application of the principle of least squares is not limited to situations in which p is normally distributed. The GaussMarkov theorem is to the effect that, among unbiased estimates which are linear functions of the observations, those yielded by least squares have minimum variance, and the independence of this property from any assumption re...

" - a Comparison between Maximum Likelihood and Generalized Least Squares in a Heteroscedastic Linear

We consider a linear model with normally distributed but heteroscedastic errors. When the error variances are functionally related to the regression parameter, one can use either maximum likelihood or generalized least squares to estimate the regression parameter. We show that maximum likelihood is much more sensitive to small misspecifications in the functional relationship between the error v...