Stat61 at Swarthmore College (fall 2022)
Textbook: Mathematical Statistics and Data Analysis, 3rd edition by John A Rice
Introduction to the mathematical theory of frequentist and Bayesian statistical inference. Topics include parameter estimation, confidence intervals and hypothesis testing, linear regression methods and some basic Bayesian methods. This course will assume you are familiar with STAT 011 topics and have some prior experience with computing. The textbook we will use in class is Mathematical Statistics and Data Analysis, 3rd edition, by John A Rice. You are expected to read along in your textbook each week according to the calendar above. The class format will begin in a traditional lecture-heavy manner (for Unit 1) but will transition gradually to include more active learning sessions than lectures towards the end of the semester (by Unit 3).
Demonstrate proficiency with the theory of probability and concept of random variables; familiarity with common distributions and transformations; ability to analytically derive moments of common distributions; understanding of central limit theorem as a theory and in practice.
Familiarity with sampling considerations and principles of experimental design; ability to plan and execute informative descriptions to accurately summarize data including graphical methods.
Proficiency with some sort of statistical analysis software.
Understand frequentist and Bayesian methods for parameter estimation and common approaches to evaluate and compare estimators.
Work with asymptotic theorems to characterize the behavior of common types of estimators.
Understand how to analytically derive a Bayesian posterior distribution and how to interpret a Bayesian credible interval and demonstrate familiarity with different types of priors.
Understand the important role of likelihood functions for hypothesis testing in both Bayesian and frequentist frameworks
Understand the relationship between frequentist confidence interval estimation and hypothesis testing.
Familiarity with common types of optimal testing strategies.
Construct and interpret frequentist p-values for hypothesis tests and interpret the error rates.
Identify/define model parameters and state statistical inferential questions in terms of these parameters for various common, realistic study settings.
Contextualize statistical methods and theory in science and policy at large and develop a habit of mind informed by the stewardly application of such methods.
Please reference this study guide and in case it’s useful, here some of my personal study tips.
Note: You can find the solution to Problem 2.b in the Unit 1 class notes on page 50.
HW 19 and HW 19 solutions
HW 20 and HW 20 solutions
HW 21 with note and HW 21 solutions
HW 22 and HW 22 solutions
Correction: In Problem 2, the R function you may want to use is “pbinom()” rather than “dbinom()”.
HW 23 and HW 23 solutions
HW 24 and HW 24 solutions