## Statistical Theory

**Math 152, Fall 2018**

Jo Hardin

2351 Millikan

jo.hardin@pomona.edu

- Homework Assignments
- class notes & HW solutions on Sakai

**Office Hours: Wed & Thurs 1:30-3:30, or by appointment**

**Mentor** **Melissa Hooke:** Thurs 8-10pm, Andrew 2161

**Mentorless** sessions: Wed 6-8pm, Millikan 2131

Exam 1 (Tuesday, 10/16/18; take home due Friday 10/19/18)

Exam 2 (Tuesday, 11/20/18; take home due in class Thursday 11/29/18)

Final Exam (Monday, 12/17/18, 2pm)

**Handouts:**

- R documentation / help
- swirl package
- DataCamp free R tutorial https://www.datacamp.com/courses/free-introduction-to-r (also: first chapter of both ggplot2 and dplyr are free and very well done)
- Google for R: http://www.rseek.org/
- R tutorial
- An Introduction to R, Venables & Smith
- R Language Definition, R Core Team
- Another tutorial, with exercises & solutions
- Mosaic Reference Guide, need to install the mosaic package
- A Student’s Guide to R; Horton, Pruim, Kaplan (click on “Raw” to download)
- Data Wrangling Cheatsheet: http://www.rstudio.com/resources/cheatsheets/

- Warm-ups & Solutions:
- WU1 – Joint Dist
- WU2 – Bayesian Posterior
- WU3 – Bayesian Estimate
- WU4 – MLE
- WU5 – MGF
- WU6 – CI
- WU7 – Fisher Information
- WU8 – Posterior Interval
- WU9 – Hyp Test 1
- WU10 – Hyp Test 2
- WU11 – Simple Hyp Test
- WU12 – MLRUMP
- WU13 – LRT (wrote out the off-the-cuff example from class)

**Homework:**

- Homework will be assigned from the text with some additional problems. One homework grade will be dropped. Homework will be done using the statistical software package R. All homework must be done in R Markdown (or R Sweave if you want to use LaTeX).
__Homework will be due on Friday by noon to the Homework box in the Math Reception office__

**Computing:**

- R will be used for homework assignments.
- We will be using R on the Pomona server: https://rstudio.campus.pomona.edu/ (All Pomona students will be able to log in immediately. Non-Pomona students need to go to ITS at Pomona to get Pomona login information.)
- In particular, http://swirlstats.com/ is a great way to walk through learning the basics of R.
- If you want to use R on your own machine, you may. Please make sure all components are updated:
- R is freely available at http://www.r-project.org/ and is already installed on college computers. Additionally, installing R Studio is required http://rstudio.org/, and all R assignments should be turned in using R Markdown.

**Participation:**

- This class will be interactive, and your participation is expected (every day in class). Although notes will be posted, your participation is an integral part of the in-class learning process. We will regularly have warm-up activities which will contribute to your participation grade. No laptop computers in class.

**Prerequisites:**

- The prerequisites for this class are Probability (Math 151 or equivalent) and completion of the sequence of calculus and linear algebra. We rely heavily on these prerequisites, and students with no background in probability or multivariable calculus will find themselves trying to catch up throughout the semester. You should be familiar with topics such as conditional probabilities and expectations, the Central Limit Theorem, moment generating functions, and probability density functions.

**Course Goals:**

- This is an introduction to mathematical statistics for students with a calculus and probability background. Though the course will be focused on the theoretical aspects of the material, there will be some real world examples in class and in the homework assignments. The goal of the course is to obtain a strong mathematical understanding of the concepts while also understanding how the concepts are used in the real world.

**Academic Honesty:**

You are encouraged to work together on homework assignments. Everything you turn in must represent your own work. Copying and pasting code (or text) from your colleagues constitutes plagiarism and will not be tolerated. All exams (including take-home) will be closed person. You may not collaborate (discuss, complain, etc.) with other individuals about the exams. Pomona’s academic honesty policy is given below and will be taken seriously.

- Pomona College is an academic community, all of whose members are expected to abide by ethical standards both in their conduct and in their exercise of responsibilities toward other members of the community. The college expects students to understand and adhere to basic standards of honesty and academic integrity. These standards include, but are not limited to, the following:
- In projects and assignments prepared independently, students never represent the ideas or the language of others as their own.
- Students do not destroy or alter either the work of other students or the educational resources and materials of the College.
- Students neither give nor receive assistance in examinations.
- Students do not take unfair advantage of fellow students by representing work completed for one course as original work for another or by deliberately disregarding course rules and regulations.
- In laboratory or research projects involving the collection of data, students accurately report data observed and do not alter these data for any reason.

**Course Goals:**

- to be able to derive the methods from introductory statistics using tools from mathematics (i.e., calculus and probability)
- to be able to justify the use of a particular method (technical assumptions).
- to be able to weigh advantages and disadvantages of different estimation techniques (e.g., bias, variability, resistance to outliers)
- to communicate results effectively.

**Advice:**

- Please feel free to stop by, email, or call if you have any questions about or difficulty with the material, the computing, the projects, or the course. Come see me as soon as possible if you find yourself struggling. The material will build on itself, so it will be much easier to catch up if the concepts get clarified earlier rather than later. Enjoy!

**Grading:**

- 20% Homework
- 25% Exam 1
- 25% Exam 2
- 25% Final Exam
- 5% Class Participation