Psychology and Brain Sciences | Introduction to Mathmatical Psychology
P605 | 25805 | Townsend
I. First half of course is devoted to signal detection theory.
Although we emphasize the statistical decision aspects, there will be
some attention to the engineering/mathematical-communications theory
approach, including ideal detector theory.
TOPICS: 1. How to calculate d' and beta. 2. Derivation of optimal
settings of decision criterion, beta. 2. Some of the classical
theorems such as: "Area under the Yes-No ROC curve = probability
correct in a 2-alternative forced choice experiment". 3. Plotting
performance in Normal-Normal coordinates. 4. Finite state (e.g.,
Blackwell's threshold model) vs. continuous state models. 5.N-signal
pattern recognition: Bayesian optimality and special cases that
include matched filters, minimum distance classifiers and more.
Psychological feature models vs. discriminant machines.
6.Multidimensional signal detection and pattern recognition. Includes
introduction to testing for perceptual independence of psychological
dimensions and features.
II. Second half of course is devoted to uncovering mental
architecture, decision mechanisms, and work-load capacity using
response times and accuracy. Includes: 1. How to test serial vs.
parallel processing as well as more complex architectures. Issues of
psychological model mimicking. 2. Assessing various stopping rules in
external (e.g., scanning a newspaper) and internal (e.g., memory
scanning) search. 3. Determining the processing capability of a
system in rapid mental operations. 4. How dependence of processing
channels affects response times, especially in parallel systems. 5.
Bringing accuracy/signal detection approaches from Part I together
with the response time methodologies in Part II to form interesting
In addition, if there is time (and over coffee or whatever, whenever
possible), we will discuss potential applications of the above
powerful methodologies to brain imaging techniques, e.g., fMRI (BOLD
signals), EEG (e.g., evoked potentials), MEG, etc.