Instructor: Ethan Levien
Course on canvas.dartmouth.edu.⇗
Course on github.io.⇗
Schedule
Week 1: Discrete Probability and Monte Carlo Simulations
Familiarity with basic concepts in probability (events, probability distribution) (Monday)
Independence and conditioning (Wednesday)
Computation: Basics of Python programming (arrays, Dataframes (moved to week 3), plotting), The concept of Monte Carlo simulation (Friday)
Week 2: iid Sums, Binomial and CLT
Expectations and variances, conditional expectation (Monday)
Binomial distribution, LLN (Monday)
Computation: Monte Carlo simulation, histogram, numerical illustration of CLT (Wednesday)
Continuous probability distributions and probability density , Central Limit Theorem and Normal distribution (Friday)
Week 3: Working with Normal RVs, Least squares LR
Properties of Normal random variables (Monday)
Single-predictor regression as conditional model (Monday)
Correlation coefficients, R-squared, regression to the mean (Wednesday)
Least squares (Wednesday)
Computation: Simulating regression models and working with tabular data (Dataframes) (Friday)
Week 4: Other aspects of single predictor LR
Computation: Finish regression examples in python, coefficient of determination
More on coefficient of determination, estimators, standard error (Wednesday/Friday)
Computation: regression with statsmodels, visualizing confidence intervals in regression (Friday)
Week 5: Hypothesis testing for LR MIDTERM (Oct 16)
Midterm review (Monday)
Introduction to regression with multiple predictors (Friday)
Computation: $p$-values, Performing multivariate regression in statsmodels and data visualization (Friday)
Week 6: Multiple predictor LR I
Effects of adding predictors to regression models (Wednesday)
Interpreting regression coefficients and model building considerations (Wednesday)
Computation: Examples in python (Wednesday)
Week 7: Multiple predictor LR II
Simpsons paradox (Monday)
Catagorical predictors/dummy variables (Monday/Wednesday)
Interactions (Wednesday)
Computation: Hands on examples in statsmodels
Week 8: Model assessment and nonlinear models
Bias variance tradeoff, overfitting, double descent (Monday)
Cross validation (Monday)
Regularization (Wednesday/Friday)
Laplace rule of succession
Week 9/10: Fourier models, Bayesian Inference, other topics
Fourier models/time series data (Monday)
Priors (Wednesday)
Laplace rule of succesion from Bayesian perspective (Wednesday)
Relationship between bayesian linear regression and regularization
The kernel trick, other topics?