Grading
Homework (10%), two midterms (25% each) and final exam (40%).

References
A number of references are on reserve in the Engineering Library (including books by Ferguson, Berger, Lehmann (2), Kay (2), Levy, Poor and Van Trees).

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 estimation; Cramer-Rao bounds; asymptotic optimality; the EM algorithm
• Monte Carlo Methods: estimation of moments and tail probabilities, importance sampling, bootstrap, random number generation, recursive Bayesian filtering.
• Advanced Topics: Robust detection and estimation; nonparametric estimation; particle filtering.