*** MEETING: Fridays 9:10-12:10 in S409 ***
Most students and researchers are familiar with linear statistical models such as ANOVA and linear regression. The advantage of linear models is that they are flexible and can be used for inference across many disciplines. They are, however, often poor models of cognitive and psychological processes.
This course is about a different class of models for psychology. Two main paths of cognitive modeling have evolved in mathematical psychology, depending on how we deal with the topic of study as a 'black box'. One path of modeling is concerned with uncovering the structure within the black box, and the other path of modeling focuses on capturing the properties of the black box by the mathematical model. This course is designed to introducing a number of models from both paths. In doing so, important general concepts of modeling, including parameter estimation and goodness-of-fit based on the likelihood principle, are introduced.
In a nutshell, in this course we will introduce some mathematical modeling approaches in psychology. We first review some basic concepts of probability and random variables. We then introduce the concept of maximum likelihood, a model-fitting approach commonly used in mathematical psychology. Some Bayesian reasoning will be introduced along the way. In the second part of the course we will introduce several applications of mathematical modeling. Possible topics include threshold theories in signal detection, multinomial processing tree models (in clinical assessment), choice models, Markov chains and random walk models, reaction time models, and Bayesian models.
We will use R, a free software environment for statistical computing and graphics that can be downloaded from the web page http://www.r-project.org/, for some of the class presentation and some of the homework problems.