In this paper, I provide a tutorial exposition on maximum likelihood estimation (MLE). The intended audience of this tutorial are researchers who practice mathematical modeling of cognition but are unfamiliar with the estimation method. Unlike least-squares estimation which is primarily a descriptive tool, MLE is a preferred method of parameter estimation in statistics and is an indispensable tool for many statistical modeling techniques, in particular in non-linear modeling with non-normal data. The purpose of this paper is to provide a good conceptual explanation of the method with illustrative examples so the reader can have a grasp of some of the basic principles
1 A Brief Review of Matrices and Vectors 1.1 Matrices 1.2 Vectors and Vector Spaces 1.3 Eigenvalues and Eigenvectors 2 A Brief Review of Probability and Random Variables 2.1 Sets and Set Operations 2.2 Relative Frequency and Probability 2.3 Random Variables 2.4 Expected Value and Moments 2.5 The Gaussian Probability Density Function 2.6 Several Random Variables 2.7 The Multivariate Gaussian Density 2.8 Linear Transformations of Random Vectors 3 A Brief Overview of Linear Systems 3.1 Introductory De®nitions 3.2 Linear System Characterization-Convolution
