課程資訊
課程名稱
心理學數理方法
MATHEMATICAL METHODS IN PSYCHOLOGY 
開課學期
99-1 
授課對象
理學院  心理學系  
授課教師
徐永豐 
課號
Psy5028 
課程識別碼
227 U0920 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期五2,3,4(9:10~12:10) 
上課地點
南館S409 
備註
限本系大三以上學生,大二或外系校生需經老師同意。需同時選修心理學資料處理-以R為例。
總人數上限:10人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/991HsuMathPsy 
課程簡介影片
 
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課程概述

***** 如果你有興趣修此門課但未能選上, 請勿缺席第一堂課. 我們會視情況更改修課人數上限. *****

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.
 

課程目標
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. 
課程要求
Students are expected to participate actively in classroom discussion, read the course material thoroughly and critically, and give presentations. 
預期每週課後學習時數
 
Office Hours
每週二 15:30~17:20 
參考書目
 
指定閱讀
There is no required textbook. All required readings are from journal papers and book chapters that will be distributed in class. 
評量方式
(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)