Grading and Policy
There will be biweekly homeworks (20%), two midterm exams (25% each) and a class project (30%).

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.
• Advanced Topics for 2009:
  • Detection/Estimation: an information-theoretic approach.
  • Graphical models and inference on graphical models.
  • Small sample set estimation and detection problems.
  • Advanced topics in large deviations theory.

Project topics: Suggested reading

• Factor graphs for detection and estimation:
  1) Factor graphs and the sum-product algorithm, Kschischang, Frey, Loeliger, 2001.
  2) Loeliger, Dauwels, Hu, Ping, Korl, and Kschischang, The factor graph approach to model-based signal processing, 2007.
  
• Good-Turing distribution estimation:
  1) The population frequencies of species, Good, 1953.
  2) Always Good-Turing, Orlitsky, Santhanam, Zhang, 2008.
  
• Compressive sensing detection and estimation:
  1) Rice compressive sensing webpage - Detection and estimation with compressive measurements, Davenport, Wakin, and Baraniuk, 2006.
  2) Rice compressive sensing webpage - Analyzing least squares and Kalman filtered compressed sensing, Vaswani, 2009.
  
• Bayesian Networks, Statistical Physics:
  1) Tutorial on Bayesian networks.
  2) Graphical models, exponential families, and variational inference, Wainwright and Wilsky, 2007.
  
  
• PROJECT ORGANIZATION: INSTRUCTIONS: DOC
  
  

Project presentations

• Prediction and Interpolation of Rayleigh Random Processes using Factor Graphs:
  Baker, Esteki, Gorell
  
• Sequential Compressed Sensing:
  Sai, Gustafson
  
• Estimating Renyi entropy under limited observations:
  Pham, Tuna
  
• Distribution estimation of two related sources:
  Huang, Farnoud, Gigaud
  
• Image Processing on Factor Graphs:
  Jiang, Jun, Lam
  
• Density Evolution for AWGN Gilbert-Elliot Channel Models:
  Freris, Tsiligkaridis
  
• Gender Recognition Using Sparse Coding Feature:
  Yang, Li, Tan
  
• Performance Comparison of Different Sampling Methods for Gibbs Measures:
  Tan, Xu, Zhu
  
• Sequential Tumor Detection via Smartl MRI Sampling:
  Aghasadeghi, Ghaderi, Hosseinabadi, Zonouz
  
  
  

• 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.