E1 244 — Detection and Estimation Theory (3:0), Jan-Apr 2018

Instructor: Aditya Gopalan, ECE 2.09, Dept. of ECE, E-mail: first-name AT iisc.ac.in

Class time: TTh 11:30—13:00

Place: ECE 1.08

Course Description: The course presents an introductory treatment of the problems of detection and estimation in the framework of statistical inference. Detection, broadly speaking, attempts to answer whether a property is satisfied, while estimation attempts to find the value of a quantity, based on observations or data. The course is theoretical in flavour, and is suitable for beginning graduate students who wish to gain a basic understanding of the tools of mathematical statistics.

Contents: Hypothesis testing, Neyman-Pearson theorem, likelihood ratio test and generalized likelihood ratio test, uniformly most powerful test, multiple-decision problems, detection of deterministic and random signals in Gaussian noise, detection in non-Gaussian noise, sequential detection, introduction to nonparametric testing. Parameter Estimation: Unbiasedness, consistency, Cramer-Rao bound, sufficient statistics, Rao-Blackwell theorem, best linear unbiased estimation, maximum likelihood estimation. Bayesian estimation: MMSE and MAP estimators, Wiener filter, Kalman filter, Levinson-Durbin and innovation algorithms.

Prerequisites: Probability/stochastic processes

Text/References:

(1) H. Vincent Poor. An Introduction to Signal Detection and Estimation (2nd Ed.). Springer-Verlag New York, Inc., New York, NY, USA, 1994.

(2) George Casella and Roger L. Berger. Statistical Inference. Duxbury Press, Pacific Grove, PA, second edition, 2002.

Grading Policy: Homework assignments (including programming exercises): 25%, Midterm exam: 25%, Final exam: 50%

Homework assignments:

Exams:

Lecture record:

• 1) [2/1/18] Introduction, Hypothesis testing

• 2) [4/1/18] Bayesian hypothesis testing

• 3) [9/1/18] Minimax hypothesis testing

• 4) [11/1/18] Minimax hypothesis testing - randomized tests

• 5) [16/1/18] Neyman-Pearson hypothesis testing

• 6) [18/1/18] Neyman-Pearson hypothesis testing

• 7) [30/1/18] Composite hypothesis testing - Bayesian criterion

• 8) [1/2/18] Composite hypothesis testing - Neyman-Pearson criterion, Uniformly and locally most powerful tests

• 9) [3/2/18] Signal detection in discrete time - coherent detection in iid noise

• 10) [6/2/18] Signal detection in discrete time - coherent detection in Gaussian noise

• 11) [8/2/18] Signal detection in discrete time - signals with random parameters, noncoherent detection of sinusoidal carrier

• 12) [13/2/18] Signal detection in discrete time - purely stochastic signals

• 13) [15/2/18] Performance evaluation of detectors - Chernoff bounds

• 14) [20/2/18] Sequential hypothesis testing framework

• 15) [22/2/18] Sequential Probability Ratio Tests (SPRTs), performance analysis of SPRTs

• 16) [27/2/18] Introduction to Estimation theory, Method of Moments estimators

• 17) [6/3/18] Maximum likelihood estimators, Bayes estimators

• 18) [8/3/18] Performance of estimators - Mean Square Error criterion, bias-variance tradeoff, Best Unbiased estimators

• 19) [13/3/18] Cramer-Rao lower bound for estimator variance, attainment of the bound

• 20) [15/3/18] Sufficient statistics, the factorization theorem, minimal sufficient statistics

• 21) [20/3/18] Best unbiased estimators and sufficient statistics, the Rao-Blackwell theorem for unbiased estimation

• 22) [22/3/18] Complete families and statistics, the Lehmann-Scheffe theorem for complete, sufficient statistics, Loss function framework for estimator performance evaluation

• 23) [27/3/18] Bayesian and minimax estimation with general losses, Consistency of the MLE

• 24) [3/4/18] Asymptotic normality of the MLE, Linear Gauss-Markov model, Kalman-Bucy filter

• 25) [5/4/18] Kalman-Bucy filter

• 26) [10/4/18] Linear minimum mean-square error (MMSE) estimation theory

• 27) [12/4/18] Levinson-Durbin algorithm for estimation of wide-sense stationary processes

Last updated: 30-May-2022, 12:24:01 IST