Session 07 - Mathematical Modeling Part 4

Super-function “Psi” + simulated experiments

Overview

Topic Duration Notes
Homework wrapup: Productive Explanations 20
Formalization: Mathematical Models Simulations 60 Slides, Steps 5+6
Group work: Create super-function + plot for individual functions 40
Homework: Think about candidate theories for your own formalization

Homework (individual / groups)

Next week, we will form (up to) four new groups that work on their own theory formalization. Please think about candidate theories that you would like to formalize. You can also team up with other students to propose a theory together.

What theory would be a good fit? (inclusion criteria)

  • A theory that is sufficiently precise and has a defined and not too large scope.
  • It explains a central phenomenon, and this phenomenon is robust (i.e., replicable and generalizable across several dimensions).
  • Its core premises are formulated in a clear and concise form on a few pages.
  • There doesn’t exist a formalized theory yet (e.g., it would be hard to re-create decades of theory building on the drift-diffusion model within a single course).

What theory would not be a good fit? (exclusion criteria)

  • You need to read three books to understand the theory.
  • The “all-encompassing theory of human nature”
  • You need a lot of expert input and judgement to fill in the gaps of the underspecified theory.
  • You need very specific domain knowledge to even understand the basic phenomena and constructs of the theory.

Deliverable: A presentation (~15 min.)

Prepare 5-7 slides (7 is the hard maximum):

  • 1 slide: Describe the central phenomenon
  • 1-2 slides: Show …
    • a typical experiment that demonstrates the phenomenon
    • the typical statistical design and analysis (e.g. “a 2x2 ANOVA”)
    • (optionally) one central results plot that shows the statistical pattern
  • 1-2 slides: Describe the explaining theory/framework
    • What are the key constructs/variables
    • What are the assumed relationships
  • 1 slide: Pros and cons, from the perspective of formalization
    • What aspects facilitate a formalization?
    • What aspects are difficult to formalize?
  • 1 slide, for reference: What is the central paper that needs to be read?