Grading and Policy
There will be six homeworks worth 10%, two midterm exams worth 50% (25% each) and a comprehensive final exam worth 40%.

Collaboration on the homeworks is permitted, however each student must write and submit independent solutions. Homework is due in the class period on the due date, unless otherwise instructed. No late homework will be accepted, unless an extension is granted in advance by the instructor.

Topics

• Elements of Statistical Decision Theory
  • A general framework for discussing the Bayes and minimax approaches to detection and estimation.
  • M-ary hypothesis testing and Bayesian parameter estimation obtained as special cases.
• Binary Hypothesis Testing
  • Bayesian decision rules.
  • Minimax decision rules.
  • Neyman-Pearson decision rules (the radar problem).
  • Composite hypothesis testing.
• Signal Detection in Discrete Time
  • Models and detector structures.
  • Performance evaluation, Chernoff bounds.
• Parameter Estimation
  • Bayesian estimation.
  • Nonrandom parameter estimation.
  • Maximum Likelihood (ML) estimation, Cramer-Rao bounds, asymptotic optimality.
• Minimum Mean Squared Error (MMSE) Estimation
  • MMSE estimation and linear MMSE estimation for random vectors (the orthogonality principle).
  • Kalman and Wiener filtering.
• Advanced Topics
  • Robust detection and estimation.
  • Nonparametric estimation.
  • Particle filtering.
  • More topics as time permits.

References

• E. L. Lehmann and J. P. Romano. Testing Statistical Hypotheses, Springer.
• E. L. Lehmann and G. Casella. Theory of point estimation, Springer.
• H. L. Van Trees. Detection, estimation, and modulation theory, Wiley.