Exam Logistics

• In the testing center from Nov 7-Nov 11.  Available from when the testing center opens on Nov 7 until it closes on Nov 11.
• 3 hour timed.
• Closed book.
• One 8.5" by 11" sheet of notes allowed.
  
• Testing center calculator required.
  
• Mix of true/false, short answer, matching, and "solve the following" problems.

• Distributions
• joint
• marginal
• conditional
• Bayes rule
• The chain rule
• product of conditional distributions
• conditional independence
• product of conditionals with parents
  
• Graphs for Bayes nets
  
• syntax
• semantics
• conditional probabilty tables
• Obtaining joint and marginal distributions from the graph and tables
• The chain rule with conditional independence
• Canonical forms
• noisy OR
• noisy AND
• Markov processes -- 1st order, 2nd order, ...
  

• State space representations
• p(s_t  | s_t-1)
  
• p(x_t  | x_t-1)
  
• p(o_t  | s_t)
• p(z_t  | x_t)
• equations for bel and \overline{bel} for both discrete and continuous random variables
• interpretations for bel and \overline{bel}
• conditional independence assumptions
• Grid filter
• states
• implementation
• applications
  

• Gaussians
• scalar and vector forms
  
• priors
• likelihoods
• posteriors
• Sequential estimates of the mean and  variance
  
• Matrix form
  
• System model: x_{t+1} = Fx_t + eta_t
  
• eta_t  ~ N(0,Sigma_x)
• Observation model: z_t = Hx_t + nu_t
•  nu_t  ~ N(0,Sigma_z)
• Sigma_0, mu_0
• P(x_{t+1} | x_t) ~ N(Fx_t,Sigma_x)
• P(z_t|x_t) ~ N(HX_t,Sigma_z)
• P(x_t|z_t) ~ N(mu_t, Sigma_t)
• Kalman filter equations: must be able to interpret and manipulate
  
• mu_t
• Sigma_t
• K_t
• Balance between system and observation noise
• Applications
• Lessons from tutorial
• Limitations
• Tradeoffs between system model, observation sensors, and noise covariance
  

• CAS representation
• evidence=observation
• states, observations, and posterior probabilities
• Equation 16.1 in the book
  
• Axioms of "well behaved" preferences
• Constructing a utility function using the "Preferences among lotteries" technique
  
• continuity
• lotteries
• algorithm
  
• Uniqueness: positive affine transformations
• Utility of money
• Expected utility
• computing expectations
• maximum expected utility
• arg max notation