## STA250(114)/MTH342(136): Statistics

 Lec: Soc Sci 136 Lab: Old Chem 01 Tue & Thu 2:50-4:05pm Wed 10:05-10:55am or 11:55am-12:45pm Prof: Robert L. Wolpert TA: Ken Van Haren, Jonathan Cohen, Anjishnu Banerjee E-mail: wolpert@stat.duke.edu krv2@stat.duke.edu, jonathan.cohen@duke.edu Office: Old Chem 211c, 684-3275 Old Chem 211a, 684-5884 OH: Wed 1:30-2:30pm Mon 4-7pm, Thu 5-8pm Tue & Thu 4:05-4:20pm (in classroom)

### Description

An introduction to the concepts, theories and methods of statistical inference. We discuss both the ideas and methods of modern Bayesian statistical science as well as the classical methods based on sampling theory. Statistics is a vast field, and a first one-semester course can offer only a brief introduction, with a deeper look at a few key ideas. The goal of this course is to provide such an introduction and to illustrate through examples how Statistics serves as the foundation for all scientific reasoning and inference amid uncertainty.

Statistical inference is like probability theory, only backwards. In probability we start with a distribution (say, the normal with specified mean μ and variance σ2) and predict features of future observations x=(x1, x2,..., xn); in statistics we observe the data x and then try to guess the distribution (or just the parameters) that generated them.

#### Prerequisites

Statistical modeling and inference depend on the mathematical theory of probability, and solving practical problems usually requires integration or optimization in several dimensions. Thus this course requires a solid mathematical background: calculus at the level of MTH212(103) or MTH222(105) and at least co-registration in linear algebra MTH221(104) or MTH216(107). Students must be proficient in calculus-based probability theory at the level of MTH230(135)/STA230(104) (we will review that material the first week of class). Here is a Diagnostic Test. If it seems easy to you then you're probably ready to take this class. Students without strong preparation in these will need to invest significant additional time to fill in the gaps. For another check, here is a recent closed-book Probability Final Exam; to take this Statistics course you should be able to complete at least 75% or so of the exam.

The course text is Morris DeGroot & Mark Schervish, Probability and Statistics (4th edn). All class materials are distributed on-line via the web; for example, you may view homework assignments (and sometimes class notes) on the Syllabus. Blackboard is used only to report scores from homeworks and examinations.

### Homework Assignments

The only way to learn statistics is to solve problems (or, in Sophocles' words, One must learn by doing the thing; for though you think you know it, you have no certainty until you try). Weekly problem sets are assigned through the on-line syllabus. Homeworks are collected at the start of each Thursday class (so I can answer questions about them in class) and are returned at the following Wednesday Lab Session, after which solutions will be posted on the web. Until solutions are posted, late homeworks are accepted but are penalized 10% per day. The lowest homework score will be dropped.

You may work with other students on the homework problems, but you must write up your final answers independently: copying homework solutions is not allowed. You are encouraged to ask me or the TA for help on your homework, after you have tried to solve the problems on your own. Questions about homework scores should first be addressed to the TA.

HELP is available! The TA and I both have office-hours (see above). In addition, the Department of Statistical Science maintains an open Help Session every Sun-Thu from 4:00-9:00 pm in the Statistical Education Center (SEC), located in room 211a Old Chem, where a statistics graduate student will be happy to help you (detailed times and staffing are listed on the SEC website). There may also be grad students from other departments, helping students in the introductory statistics courses--- be sure to find a Statistical Science PhD student (labeled "All courses") or major (labeled "114 and below") to help for this course. Consult the TA Schedule for times.

### Exams

In-class Midterm Exams and Final Exam are all closed-book. You may bring one 8½"×11" sheet of paper to each exam with anything you want written on it; the exam will include this sheet of common pdf and pmf formulas. You may (and probably should) bring to each exam a calculator capable of computing exponentials, logarithms, and factorials (no laptops, netbooks, or cellphones, however). Questions about exam scores should be taken up with the Professor. As an aid to study, here are some past exams:
 Spring 2009: 1st Midterm 2nd Midterm Final Exam
Solutions for these are not made available, because their value is lost if students peek at the answers when they get stuck. Read your class notes and the text when you're stuck; check with me or the TA if you need a hint, or if you aren't sure if your solution is correct.

Course grades are based on two in-class Midterm Exams (20% each), ten weekly Homework assignments (20% total), and a cumulative Final Exam (40%). Late homeworks are penalized, and missed homeworks receive zero scores, but each student's lowest homework score is dropped. Histograms and summary statistics of midterm and final exam scores will be added to the syllabus web page. Brief in-class quizzes will be added if needed. Each student's current average and course standing are available from the instructor at any time.