Students are required to attend class sessions and studio sessions, the latter of which take place on Friday. Typically, studio sessions are used to introduce longer problems and the use of R.

WEEK # | SES # | TOPICS | READINGS | SLIDES | PROBLEM SETS |
---|---|---|---|---|---|

Probability | |||||

1 | C1 | Introduction, counting and sets | |||

C2 | Probability basics | ||||

S1 | Birthday matches; Introduction to R | ||||

2 | C3 | Conditional probability, Bayes' theorem | 3: Conditional Probability, Independence and Bayes' Theorem (PDF) | ||

C4 | Discrete random variables, expectation | 4a: Discrete Random Variables (PDF) | |||

S2 | Expectation; Simulation using R | ||||

3 | C5 | Variance, continuous random variables | 5a: Variance of Discrete Random Variables (PDF) | ||

S3 | Gallery of continuous variables, histograms | 5c: Gallery of Continuous Random Variables (PDF) | |||

4 | C6 | Expectation, variance, law of large numbers and central limit theorem | 6a: Expectation, Variance and Standard Deviation for Continuous Random Variables (PDF) 6b: Central Limit Theorem and the Law of Large Numbers (PDF) | ||

C7 | Joint distributions: independence, covariance and correlation | 7a: Joint Distributions, Independence (PDF) | |||

S4 | Covariance, correlation, CLT | ||||

5 | C8 | Review for exam 1 | |||

C9 | Exam 1 | ||||

Statistics: Bayesian Inference | |||||

5 | C10 | Introduction to statistics; maximum likelihood estimates | 10a: Introduction to Statistics (PDF) | ||

6 | C11 | Bayesian updating with known discrete priors | |||

C12 | Bayesian updating: probabilistic prediction; odds | 12a: Bayesian Updating: Probabilistic Prediction (PDF) | |||

S5 | Bayesian updating | ||||

7 | C13 | Bayesian updating: continuous prior, discrete data | |||

C14 | Beta distributions: continuous data | ||||

S6 | Continuous data, continuous priors | ||||

8 | C15 | Conjugate priors; choosing priors | |||

C16 | Probability intervals | ||||

S7 | No studio | ||||

Statistics: Frequentist Inference—Null Hypothesis Significance Testing (NHST) | |||||

9 | C17 | Frequentist methods; NHST | 17a: The Frequentist School of Statistics (PDF) | ||

C18 | NHST II: Significance level, power, t-tests | ||||

S8 | Rejection regions; NHST | ||||

10 | C19 | NHST III: Gallery of tests | |||

C20 | Comparison of Bayesian and frequentist inference | 20: Comparison of Frequentist and Bayesian Inference (PDF) | |||

S9 | NHST; comparing frequentist and Bayesian methods | ||||

11 | C21 | Review for exam 2 | |||

S10 | Exam 2 | ||||

Statistics: Confidence Intervals; Regression | |||||

12 | C22 | Confidence intervals for normal data | |||

C23 | Confidence intervals II | 23a: Confidence Intervals: Three Views (PDF) 23b: Confidence Intervals for the Mean of Non-normal Data (PDF) | |||

S11 | Confidence intervals III | ||||

13 | C24 | Bootstrap confidence intervals | |||

C25 | Linear regression | ||||

S12 | Bootstrapping; linear regression | ||||

14 | C26 | Review for final exam | |||

C27 | Review for final exam, cont'd | ||||

15 | Final exam |