E1 244 — Detection and Estimation Theory (3:0), JanApr 2019
Instructor: Aditya Gopalan, ECE 2.09, Dept. of ECE, Email: firstname 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, NeymanPearson theorem, likelihood ratio test and generalized likelihood ratio test, uniformly most powerful test, multipledecision problems, detection of deterministic and random signals in Gaussian noise, detection in nonGaussian noise, sequential detection, introduction to nonparametric testing. Parameter Estimation: Unbiasedness, consistency, CramerRao bound, sufficient statistics, RaoBlackwell theorem, best linear unbiased estimation, maximum likelihood estimation. Bayesian estimation: MMSE and MAP estimators, Wiener filter, Kalman filter, LevinsonDurbin and innovation algorithms.
Prerequisites: Probability/stochastic processes
Text/References:
(1) H. Vincent Poor. An Introduction to Signal Detection and Estimation (2nd Ed.). SpringerVerlag 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:

Homework 1 posted 17/1/19, Due on 31/1/19

Homework 2 posted 31/1/19, Due on 14/2/19

Homework 3 posted 14/2/19, Due on 28/2/19

Homework 4 posted 8/3/19, Due on 21/3/19

Homework 5 posted 2/4/19, Due on 16/4/19

Homework 6 posted 23/4/19 (for practice only, will not be graded)
Exams:

Midterm exam: Tuesday 5/3/19, 11:3013:00 [Midterm exam] [Solutions]

Final Exam: Tuesday 30/4/19, 09:0012:00 [Final exam] [Solutions]
Lecture record:

1) [3/1/19] Introduction, Hypothesis testing

2) [8/1/19] Bayesian hypothesis testing

3) [15/1/19] Minimax hypothesis testing

4) [17/1/19] Minimax hypothesis testing

5) [19/1/19] NeymanPearson hypothesis testing

6) [22/1/19] NeymanPearson hypothesis testing

7) [24/1/19] Composite hypothesis testing — Bayesian criterion

8) [29/1/19] Composite hypothesis testing — NeymanPearson criterion

9) [31/1/19] Signal detection — known signals in iid noise

10) [5/2/19] Signal detection — locally optimum coherent detection, coherent detection in general Gaussian noise

11) [7/2/19] Signal detection — signals with random parameters, envelope detector

12) [12/2/19] Signal detection — performance analysis of the envelope detector

13) [14/2/19] Signal detection — completely random signals, energy detector

14) [19/2/19] Sequential detection

15) [26/2/19] Sequential detection — SPRTs and Wald’s approximations

16) [7/3/19] Performance analysis of detectors — Chernoff bounds

17) [9/3/19] Introduction to estimation, Method of moments estimators

18) [12/3/19] Maximum likelihood estimators, Bayes estimators

19) [14/3/19] Meansquare error for estimators, Best unbiased estimators

20) [26/3/19] CramerRao Lower bound for unbiased estimation

21) [28/3/19] Sufficient statistics

22) [30/3/19] Minimal sufficient statistics

23) [2/4/19] RaoBlackwell theorem, Complete statistics, LehmannScheffe theorem

24) [4/4/19] Asymptotic performance — consistency and asymptotic efficiency of MLEs

25) [6/4/19] General decision theory framework for estimators, conditional expectation as the optimal MMSE estimator

26) [9/4/19] State estimation in linear dynamical systems, KalmanBucy filter

27) [11/4/19] KalmanBucy filter, Linear MMSE estimation theory

28) [13/4/19] YuleWalker equations, LevinsonDurbin filter
Last updated: 23Feb2023, 15:23:50 IST