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May 13, 2024
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PSY 7360 - Mathematical Modeling of Cognition
Formal modeling is an essential research tool in cognitive psychology and cognitive science. In this seminar we shall discuss and critically evaluate a wide variety of key formal models and modeling approaches to cognition (e.g., algebraic, geometric, analytic, qualitative, statistical, probabilistic, computational, connectionist, dynamical, structural, and process). We shall do this with three goals in mind: 1) to become aware of the wide range of modeling techniques at our disposal, 2) to achieve a basic understanding of these techniques and the modeling process in general, and 3) to get us to start thinking strategically and analytically about how to construct an effective formal model (i.e., one that predicts and explains our empirical results). Discussions will assume no previous modeling background.
Requisites: PSY 6310
Credit Hours: 3
Repeat/Retake Information: May not be retaken.
Lecture/Lab Hours: 3.0 seminar
Grades: Eligible Grades: A-F,CR,PR,WP,WF,WN,FN,AU,I
Learning Outcomes:
- Carry out computations for each example given after being presented with the formal model.
- Define at least three models of a mathematical function and define the following concepts: homomorphism, isomorphism, automorphism, and endomorphism.
- Describe and explain Luce’s four tensions between mathematical models in Psychology.
- Describe and explain at least five key factors to consider when evaluating a cognitive model.
- Describe and explain key formal modeling examples from the following cognitive areas: memory, similarity, attention, categorization, learning, perception, and decision making.
- Describe and explain the various roles of parameters in models and describe at least two methods for estimating parameters.
- Describe at least two methods for evaluating the performance of a cognitive model.
- Explain how the concepts above are important in our understanding of measurement theory and mathematical modeling
- Explain what a cognitive model is and describe the typical steps in the model building process.
- Identify and explain at least five formal approaches associated with different kinds of models.
- State, explain, and prove the representation theorem for ordinal measurement.
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