**Week 1: Introduction to probability and computation**

**A first look at basic discrete probability, how to interpret it, what probability spaces and random variables are, and how to code these up and do basic simulations and visualizations.**

**Week 2: Incorporating observations**

**Incorporating observations using jointly distributed random variables and using events. Three classic probability puzzles are presented to help elucidate how to interpret probability: Simpson’s paradox, Monty Hall, boy or girl paradox.**

**Week 3: Introduction to inference, and to structure in distributions **

**The product rule and inference with Bayes' theorem. Independence-A structure in distributions. Measures of randomness: entropy and information divergence. Mini-project: movie recommendations.**

**Week 4: Expectations, and driving to infinity in modeling uncertainty**

Expected values of random variables. Classic puzzle: the two envelope problem. Probability spaces and random variables that take on a countably infinite number of values and inference with these random variables.

**Week 5: Efficient representations of probability distributions on a computer**

Introduction to undirected graphical models as a data structure for representing probability distributions and the benefits/drawbacks of these graphical models. Incorporating observations with graphical models.

**Week 6: Inference with graphical models, part I**

Computing marginal distributions with graphical models in undirected graphical models including hidden Markov models. Mini-project: robot localization, part I.

**Week 7: Inference with graphical models, part II**

Computing most probable configurations with graphical models including hidden Markov models. Mini-project: robot localization, part II.

**Week 8: Introduction to learning probability distributions**

Learning an underlying unknown probability distribution from observations using maximum likelihood. Three examples: estimating the bias of a coin, the German tank problem, and email spam detection.

Week 9: Parameter estimation in graphical models

Given the graph structure of an undirected graphical model, we examine how to estimate all the tables associated with the graphical model.

**Week 10: Model selection with information theory**

Learning both the graph structure and the tables of an undirected graphical model with the help of information theory. Mutual information of random variables.

**Week 11: Final project part I**

Mystery project

**Week 12: Final project part II**

Mystery project, cont’d