Psychology and Brain Sciences | Intro to Mathematical Psychology
P605 | 28345 | Townsend, J.

The over-riding theme of the course is introduction to the modeling
of sensory, perceptual, and elementary cognitive phenomena. The
emphasis is on analytical modeling, with training in derivations and
proving central theorems in the science of discovering what goes on
in the human (or animal) black-box.  Naturally though, software such
as Mathematica and MATLAB come in handy in performing computations
that illustrate predictions, fitting real or artificial data with
models and the like.  The covered topics are being increasingly
employed by clinical scientists in exploring how patient groups
might or might not differ from control groups in elementary
perception and cognition, with detection, recognition, and memory or
visual search serving as examples.  The theory-driven methodologies
are also being incorporated in other applied settings such as human
performance in industrial and military settings.

I. The first half of the 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. The second half of the 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.  The evolution of the
strategically valuable concept of selective influence, where the
student learns about manipulation of experimental variables to
discover the underlying architecture and nature of information
processing.  3. Assessing various stopping rules in external (e.g.,
scanning a newspaper) and internal (e.g., memory scanning) search.
4. Determining the processing capability of a system in rapid mental
operations.  5. How dependence of processing channels affects
response times, especially in parallel systems.  6. Bringing
accuracy/signal detection approaches from Part I together with the
response time methodologies in Part II to form interesting dynamic

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.