1. Course character and objectives

Course objectives

At a conceptual level:

• Master the basic concepts associated with probability models
• Be able to translate models described in words to mathematical models
• Understand the main concepts and assumptions underlying Bayesian and classical inference
• Obtain some familiarity with the range of applications of inference methods

At a more technical level:

• Become familiar with basic and common probability distributions
• Learn how to use conditioning to simplify the analysis of complicated models
• Have facility manipulating probability mass functions, densities, and expectations
• Develop a solid understanding of the concept of conditional expectation and its role in inference
• Understand the power of laws of large numbers and be able to use them when appropriate
• Become familiar with the basis inference methodologies (for both estimation and hypothesis testing) and be able to apply them
• Acquire a good understanding of two basic stochastic processes (Bernoulli and Poisson) and their use in modeling
• Learn how to formulate simple dynamical models as Markov chains and analyze them

How do we do it:

• To achieve working knowledge, we:
  • cover more material than usual
  • capitalize on effective organization of the material

What this class is not:

• Not a lay science introduction/ overview of probability