On the history of maximum likelihood in relation to inverse probability and least squares

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 decoding and integer least-squares: The expected complexity

The problem of finding the least-squares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The problem is equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In...

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...

morphology, geochemistry, mineralogy, and micromorphology of soils of hormozgan province in relation to parent materials

ویژگی های زمین شیمیایی، کانی شناسی، و میکرومورفولوژیکی خاک ها و سنگ مادر مربوطه در منطقه بین بخش های جنوبی زاگرس و خلیج فارس تا دریای عمان(استان هرمزگان، ایران) مورد بررسی قرار گرفت. هدف های این مطالعه شناسایی تغییرات در خصوصیات فیزیکی، شیمیایی، و ترکیب کانی شناسی خاک، مطالعه میکرومورفولوژی و تکامل خاک، و بررسی توزیع عنصر خاک بر اساس هوازدگی، پروسه های خاک و زمین شناسی جهت توصیف اثرات مواد مادر...