## Studying for the Final

The final will cover the main ideas from class. The test is taken strongly from the homework and labs, but there are a couple of thinking questions. Here is what you can expect:

# Basic ideas from probability and statistics

1. Random variables, notation
2. Joint, marginal, and conditional probabilities and densities (see foundations homework)
3. Expectations and Moments (see mom homework)
4. Estimators, especially MOM and MLE's (see mom homework)
5. Changing variables (finding densities of a function of a random variable)

# Bayes

1. Bayes law itself (see foundations homework)
2. Bayes nets
3. Chain rule and Chain rule for Bayes nets and the formation of the joint from a net (see pruning lab)
4. Conjugacy, Prior's and Posterior's (see poisson homework)

# Graphical Models

1. d-separation (see pruning)
2. pruning (see pruning)

# Estimation

For all of these you should know how they work in both theory and practice.

1. Gibbs, including the complete conditional (see Gibbs homework and the mcmc lab)
2. Metropolis and Metropolis-Hastings (see mcmc lab)
3. Filters (see, ah yes, the filters lab)

# Decisions

1. See the decisions lab. You should be able to do the discrete case. You should understand how the derivation of the continuous case works, but you do not need to memorize the details.