# When Statistics Embraces A.I.

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### Syllabus

Instructor: Professor Xiao Wang

Office: MATH 514

Email: wangxiao@purdue.edu

Office Hour:  By Appointment Only

Lecture Time and Location: Tuesday, Thursday 12:00 pm --- 1:15pm, University 001

Note: Please include “STAT 528” in the subject line when contacting me via email. Due to the large amount of daily emails I receive, your emails may be missed if they do not include “STAT528” in the subject line.

E-mail: haow@purdue.edu

Required Textbook: Theoretical Statistics: Topics for a Core Course, by Robert Keener

Schedule: Aug 11, 2017—Dec 09, 2017

Policy: You are allowed, and even encouraged, to work with other students on the homework problems. Copying of homework, however, is absolutely forbidden and constitutes a violation of the Honor Code; therefore, each student must produce his or her own homework to be handed in and graded. You are also encouraged to ask me or the grader for help on homework problems after you have tried to solve the problems on your own.

Exam: There will be one evening midterm and one final. No Makeup Exam unless you have legitimate excuses.

Final Grade: Your final grade will depend on the following components with these proportions:  homework (30%), midterm (30%), and final exam (40%). The percentage grades needed to achieve an A, B, C, D, or F will follow approximately the following scale:  85 – 100 = A, 70 – 84 = B, 55 – 69 = C, 50 – 54 = D, 0 – 49 = F. This course has "+" and "-" scores.

Outline:

1. Probability and Measure Ch1
2. Basics
• Exponential Family Ch2
• Risk, Sufficiency, completeness, and Ancillary Ch3
• Unbiased Estimator Ch4
• Conditional Distribution Ch6
3. Bayesian Estimation
• Bayesian Estimation Ch7
• Bayesian Inference Ch15
4. MLE
• A Large Sample Theory Ch8
• Estimating Equations and ML Ch9
5. Empirical Bayes and Shrinkage Estimators Ch11
6. Hypothesis Testing
• Basic Ch12
• Higher dimension Ch13 (if time permits)
• Likelihood Ratio Test Ch17 (if time permits)