aiexperts/math-392

A course in mathematical statistics at Reed College.

Mathematical Statistics

Math 392 | Reed College | Spring 2018

Schedule

Week 1: Intro

Monday

• Parameters and statistics
• Example: stratified sampling
• Reading: p. 1-10, 13 - 20, 339 - 340
• Please join the slack group.

Wednesday

• CDFs, ECDFs
• Permutation tests
• Reading: p. 20 - 30, 35 - 48

Friday

• Bring laptops
• Activity: stratified sampling and simulation
• Permutation tests
• Reading: p. 48 - 68

Week 2: Permutation Tests

Monday

• Permutation tests
• Choice of statistics
• Reading: p. 42 - 52

Wednesday

• Contingency tables
  • Fisher's Exact
  • Permutation Chi-squared
  • Chi-squared approximation
• Reading: p. 52 - 68

Friday

• Sampling Distributions
• Central Limit Theorem
• Reading: p. 77 - 92

Week 3: Sampling Distributions and the Bootstrap

Monday

• Sampling distributions
  • Simulation
  • Exact
• Reading: p. 77 - 92

Wednesday

• Sampling distributions
  • Large Sample Approximation
• Bootstrap I
• Reading: p. 99 - 113

Friday

• Bootstrap II
• Reading: p. 113 - 129

Week 4: Estimation

Monday

• Exam I
• This week's problem set will be due next Friday.

Wednesday

• Likelihood I
• Reading: p. 52 - 68

Friday

• Likelihood II
• Reading: p. 77 - 92

Week 5: Estimation, cont.

Monday

• Method of Moments
• Properties of Estimators I
  • Bias
• Reading: p. 146 - 151

Wednesday

• Properties of Estimators II
  • Efficiency
  • Mean Squared Error
  • Consistency
• Reading: p. 151 - 157

Friday

• Simulating from f
  • Inverse Transform Method
  • Rejection Sampling
• Properties of Estimators III
  • Consistency, cont
• Reading: p. 157 - 160
• Problem set 5 due next Friday

Week 6: Confidence Intervals

Monday

• Confidence Intervals via Pivots
• Reading: p. 167 - 177

Wednesday

• Confidence Intervals via the Bootstrap
• Reading: p. 178 - 200

Friday

• Classical Hypothesis Tests
• Reading: p. 211 - 221

Week 7: Tests and Power

Monday

• Errors and Power
• Reading: p. 167 - 177

Wednesday

• Practice with Power
• Exam II review

Friday

• Exam II
• Problem set 6 due next Monday

Week 8: Linear Models

Monday

• Review Exam II

Wednesday

• Parameters for multiple variables
  • Covariance
  • Correlation
• Introduction of the Linear Model
• Reading: p. 247 - 265

Friday

• The Linear Model in high dimensions
• The Hat Matrix
• Reading: p. 247 - 279
• Problem set 6 due Monday

Week 11: Bayes I

Monday

• Large Sample Theory for the MLE

Wednesday

• Foundations of Bayesian Statistics
  • Discrete binomial
  • Beta-binomial model
• Reading: p. 316-322, (What is Bayesian Statitistics)[http://people.math.umass.edu/~lavine/whatisbayes.pdf] - Lavine

Friday

• Reading: