This course is a graduate level introduction to probability and mathematical statistics. The course discusses classic tools to extract and evaluate evidence from data, which are the basis for modern scientific discovery. The emphasis is on general ideas, such as maximum likelihood estimation and likelihood ratio tests. Special cases, like the z-test or t-test, are discussed as examples of these general approaches.
Tuesday and Thursday from 8:00 am to 9:45 pm at Engineering 2, Room 194.
Name: Abel Rodriguez, abel at ams dot ucsc dot edu
Office: Baskin Engineering, 147
Instructor Office Hours:
Tuesdays and Thursdays from 4:00 pm to 5:00 pm
We will follow Casella and Berger, Statistical Inference, Second Edition, Duxbury (CB). For some lectures I will use slides, which will be available from the class schedule below. These slides contain only remarks and main ideas, they are designed for you to take notes!!! Finally, we might use some web-based resources that I will be adding as they become necessary.
There will be five homeworks, which can be found below as part of the class schedule. The homework will not be graded, but a substantial part of each of the quizzes and exams will be taken from them.
Two quizzes, each worth 15% of the final grade.
Tuesday, October 19 during regular class hours.
Thursday, November 23 during regular class hours.
One midterm, worth 30% of the final grade.
Tuesday, November 03 during regular class hours.
The final is worth 40% of the final grade.
Thursday, December 09 between 8:00am and 11:00 am at E2-194.
Th 09/23 – No class. (slides)
Tu 09/28 – Probability theory (CB 1.1 - 1.3). (class notes)
Th 09/30 – Probability theory, cont. Transformations and expectations. (CB, 1.4 - 1.6, 2.1 - 2.4). (class notes)
Tu 10/05 – Common families of distributions (CB, 3.1 – 3.2). (class notes)
Tu 10/12 – Common families of distributions, cont. Multiple random variables (CB, 3.5 - 3.6, 4.1 – 4.3). (class notes)
Th 10/14 – Multiple random variables, cont. (CB, 4.5 - 4.7). (class notes)
Th 10/21 – Point estimation (CB, 7.1, 7.2.1-7.2.2). No class.
Tu 10/26 – Point estimation, cont. (CB, 7.3). (class notes)
Th 10/28 – Catch-up/Review. (class notes)
Tu 11/09 – Hypothesis testing (CB, 8.1-8.2).
Th 11/11 – No class. Veteran’s day.
Th 11/25 – No class. Thanksgiving.
Tu 11/30 – Asymptotic evaluations (CB, 10.3 - 10.4). (class notes)