Probability Module Guide

This module is intended to teach the basics of probabilistic thinking and estimation of probabilities. We do not assume any prior exposure to probability theory, but the review will be useful for those who do know something about it.

The abilities you should come away from this module with are:

  1. To create and reason about discrete probability models.
  2. To manipulate discrete probability expressions and to demonstrate the validity of the rules for manipulating them.
  3. To estimate parameters of probability distributions using maximum likelihood (ML) or Bayesian estimators and to explain the difference between them.
  4. To define conjugate priors and explain their role in Bayesian parameter estimation.
  5. To use the expectation maximization (EM) and Gibbs sampling frameworks to estimate probabilities in the presence of hidden variables and to explain the difference between them.

Before each class, you should study the assigned sections of the printed lecture notes and read the corresponding sections of Probability and Statistics by Morris de Groot. The lecture notes are not meant as a substitute for a textbook, but rather to highlight some of the most important and relevant material from the textbook.

There are exercises to do at home in advance of each class. These will not be collected. Instead, we will have similar exercises for you to do in class and turn in for a grade. The process of doing the exercises in class is intended to be a learning experience, but there won't be enough time for you to get much out of it unless you have already studied the text and struggled with the homework problems.

Day 0

In Class

Before the next class

Read and think about:

Day 1

In Class

Before the next class

Read and think about: Practice To turn in: Optional:

 

Day 2

In Class

Before the next class

Read and think about Practice To turn in: Optional:

Day 3

In Class

Before the next class

Read and think about Practice: To turn in: Optional:

Day 4

In Class

Before the next class

Read and think about Practice: To turn in: Optional:

Day 5

In Class

Before the next class

Read and think about Optional: To turn in:

Day 6

In Class

Before the next class

Read and think about Turn in before class on Day 8.

Day 7

In Class

Before the next class

Read and think about To turn in:

Day 8

In Class

Before the next class