課程資訊

MATHEMATICAL METHODS IN PSYCHOLOGY

99-1

Psy5028

227 U0920

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/991HsuMathPsy

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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. For example, researchers may be interested in assessing the roles of storage and retrieval processes in a memory task. The relationship between storage and retrieval is surely not linear.

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 'black box.' One path of modeling is concerned with uncovering the structure within the black box; it aims to provide detailed, substantive, and formal accounts of specific mental processes. The other path of modeling focuses on capturing the properties of the black box by the mathematical model; it aims to provide the representation that might characterize a large family of processing models. This course is designed to cover a limited number of models from both paths. In doing so, important general concepts in modeling are introduced.

One of the goals is to teach students a unified principle for all statistics: likelihood. We will show you how to write down likelihoods of various models and how to use computational techniques to maximize likelihood. We will also mention issues on model selection based on nested likelihood and others. Moreover, since simulation can help developing insight about how models account for phenomena, we will use simulations in this regard from time to time.

To summarize, 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. In the second part of the course we illustrate the use of mathematical methods with examples from psychophysics. Several applications of mathematical modeling also will be introduced. Topics include signal detection theory, threshold models, multinomial processing tree models, etc.

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 homework problems.

The goal is to introduce some mathematical modeling approaches in psychology. Also, general concepts of probability, random variables, likelihood, and goodness of fit will be introduced.

Students are expected to participate actively in classroom discussion, read the course material thoroughly and critically, and give presentations.

Office Hours

There is no required textbook. All required readings are from journal papers and book chapters that will be distributed in class.

(僅供參考)

 No. 項目 百分比 說明 1. Quiz 30% 2. Class presentation and participation 20% 3. Homework 30% 4. Midterm 20%

 課程進度
 週次 日期 單元主題 第1週 09/17 Course Intro 第2週 09/24 Sample space; Events; Probability measure 第3週 10/01 Conditional probabilities; Bayes theorem 第4週 10/08 (Quiz) Random variables; Distribution functions; Discrete and Continuous distributions 第5週 10/15 Law of large numbers; Central limit theorem; etc. 第6週 10/22 Sampling mean and sample variance; chi-square, t, F stats 第7週 10/29 (Quiz) Chapter 1 第8週 11/05 The maximum likelihood principle; Chapter 2 第9週 11/12 Chapter 3 第10週 11/19 R session led by TA 第11週 11/26 Midterm 第12週 12/03 Chapter 4 第13週 12/10 The theory of signal detectability (Ch. 6 from the Coombs, Dawes, & Tversky 1970 book) 第14週 12/17 Chapter 5 第15週 12/24 Chapter 6.1 & 6.2; Confidence ratings in SDT vs. in Threshold theory 第16週 12/31 Chapter 6.3; Multinomial processing tree models (i) 第17週 01/07/2011 Multinomial processing tree models (ii)