Type of Credit: Elective
Credit(s)
Number of Students
貝氏統計不論在學術研究或實務應用上都獲得相當大的成功，它也是目前AI領域中倚重甚深的運算技術。除了國際期刊推荐以貝氏統計取代傳統統計，科技公司例如Google, 臉書,和微軟也應用貝氏統計來分析消費者行為。因此，培養學生認識乃至於精熟貝氏統計方法是件刻不容緩的事。本課程的設計包括，貝氏統計方法的基礎概念、機率分配、貝氏推論、貝氏模擬、貝氏潛在類別分析、貝氏階層線性模型、貝氏項目反應理論、以及狄利克雷歷程混合模型。課程中也將教授學生如何使用程式語言R與JAGS實作貝氏統計分析。這些基礎概念和應用程式練習將幫助學生提昇應用技能，能夠在短時間內進階到國際水準。本課程內容可能會隨進度略有調整，請以實際上課情形為準。
能力項目說明
本課程目標為 (1) 培養學生具備貝氏統計分析的觀念， (2) 協助學生了解貝氏統計的基本原理， (3) 訓練學生能實際使用貝氏統計方法進行資料分析與模型比較。為此，本課程除了貝氏統計的數理基礎之外，也將要求學生全程使用R語言與JAGS套件進行貝氏統計分析。因此，同學修習本課之後將具備以貝氏統計方法分析資料的能力，以及良好的R語言程式撰寫能力。這兩種能力都是目前資料科學與機器學習領域中被強烈要求的。
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
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週次Week |
課程主題Course Theme |
課程內容與指定閱讀Content and Reading Assignment |
教學活動與作業Activity and Homework |
學習投入時數Estimated time devoted to coursework per week |
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課堂講授Lecture Hours |
課程前後Preparation Time |
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1 |
Introduction |
Credibility, Model, and Parameters |
Practice to interpret a statistical question in a Bayesian way |
3.0 |
6.0 |
|
2 |
R basics and Bayes' theorem |
R commends for different probability distributions and basic concepts of Bayes' theorem |
Homework: Use R to make histogram with the data randomly sampled from different probability density function (z, t, F, and chi-square) |
3.0 |
5.0 |
|
3 |
AI related issues |
AI ethics, fairness, and robustness |
No homework |
3.0 |
3.0 |
|
4 |
National Day |
|
|
|
|
|
5 |
Markov Chain Monte Carlo method |
The principle of MCMC method and maximum likelihood |
Homework: Practice how to do modeling with MCMC method |
3.0 |
7.0 |
|
6 |
Parameter estimation - Binomial distribution |
Estimate the parameter of Binomial distribution |
Homework: Practice how to estimate the parameter of a Binomial distribution |
3.0 |
9.0 |
|
7 |
Parameter estimation -normal distribution |
Estimate the parameters of normal distribution |
Homework: Practice how to estimate the parameters of a normal distribution |
3.0 |
9.0 |
|
8 |
Parameter estimation - t distribution |
Estimate the parameters of t distribution |
Homework: Practice how to estimate the parameters of a t distribution |
3.0 |
6.0 |
|
9 |
Midterm examination week |
Oral report for your project in class |
Oral report for your project in class |
3.0 |
9.0 |
|
10 |
Regression and ANOVA in Bayesian style |
Estimate the parameters of general linear model |
Homework: Do regression analysis and ANOVA in Bayesian style |
3.0 |
6.0 |
|
11 |
Cognitive modeling in Bayesian style |
Introduce how to fit a cognitive model to real data |
Homework: Practice how to do cognitive modeling in Bayesian style |
3.0 |
9.0 |
|
12 |
Bayes factor and model comparison |
Model comparison in Bayesian framework |
Homework: Practice how to compare two models in Bayesian framework |
3.0 |
9.0 |
|
13 |
Bayesian latent class analysis |
Introduction to how to extract latent classes in a data set |
Homework: Practice how to fit a Bayesian LCA model and choose the number of latent classes. |
3.0 |
6.0 |
|
14 |
Hierarchical linear modeling (aka mixed-effects model) |
Introduction to how to implement hierarchical Bayesian linear model |
Homework: Practice how to fit a Bayesian hierarchical linear model using the MathAchieve dataset. |
3.0 |
6.0 |
|
15 |
Item Response Theory (IRT) in Bayesian style |
Implement a Partial Credit IRT model. |
Homework: Practice how apply Bayesian inference to estimating parameters in the models of IRT |
3.0 |
6.0 |
|
16 |
Bayesian Nonparameterics by Dirichlet Process Mixtures |
Introduction to nonparametric Bayesian method, Dirichlet process, and Dirichlet process mixture model |
Homework: Practice how to implement Dirichlet Process Mixture Model |
3.0 |
6.0 |
|
17 |
Oral presetnation I |
Presenting your project in virtual class |
Homework: Prepare your presentation slides and other necessary materials for your project |
3.0 |
9.0 |
|
18 |
Oral presentation II |
Presenting your project in virtual class |
Homework: Prepare your presentation slides and other necessary materials for your project |
3.0 |
9.0 |
作業和專案為評分依據。
其中，完成度、嚴謹度各佔每次作業及專案的50%。
Kruschke, J. K. (2014). Doing Bayesian Data Analysis (Second Edition) A Tutorial with R, JAGS, and Stan.
Lee, M. D., & Wagenmakers, E.-J. (2014). Bayesian Cognitive Modeling: A Practical Course. Cambridge University Press, UK.