Hudson Derek J. Statistics lectures II: Maximum likelihood and least squares theory

Geneva: CERN, 1964. — 116 p.This set of eight lectures follows directly on the introductory “Lectures on elementary statistics and probability”, by the same author, published as a yellow report CERN 63-29. In the present volume, the emphasis is on a fairly thorough examination of a few more advanced problems, so as to indicate how the argument is carried through from first principles.
A problem in hypothesis testing is solved by using the t distribution; probability paper is used to test for a normal distribution; the F distribution is defined and its density function is derived.
The principle of maximum likelihood is introduced from the intuitive point of view of trying to find the most explanation of the experimental data observed. The graphs of several likelihood functions are sketched, most of them on a logarithmic scale. Bayes Theorem shows how the likelihood function should be modified when prior information about parameters is available.Application of the t distribution
Analysis of the assumptions made
The F distribution
Maximum Likelihood
Graphical analysis of the likelihood
The likelihood of two parameters
Bayesian inference
Early history of least squares
Least squares and regression analysis
Orthogonal polynomials
Normal regression analysis