E1 244 — Detection and Estimation Theory (3:0), Jan-Apr 2019
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:
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Homework 1 posted 17/1/19, Due on 31/1/19
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Homework 2 posted 31/1/19, Due on 14/2/19
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Homework 3 posted 14/2/19, Due on 28/2/19
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Homework 4 posted 8/3/19, Due on 21/3/19
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Homework 5 posted 2/4/19, Due on 16/4/19
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Homework 6 posted 23/4/19 (for practice only, will not be graded)
Exams:
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Midterm exam: Tuesday 5/3/19, 11:30-13:00 [Midterm exam] [Solutions]
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Final Exam: Tuesday 30/4/19, 09:00-12:00 [Final exam] [Solutions]
Lecture record:
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1) [3/1/19] Introduction, Hypothesis testing
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2) [8/1/19] Bayesian hypothesis testing
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3) [15/1/19] Minimax hypothesis testing
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4) [17/1/19] Minimax hypothesis testing
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5) [19/1/19] Neyman-Pearson hypothesis testing
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6) [22/1/19] Neyman-Pearson hypothesis testing
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7) [24/1/19] Composite hypothesis testing — Bayesian criterion
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8) [29/1/19] Composite hypothesis testing — Neyman-Pearson criterion
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9) [31/1/19] Signal detection — known signals in iid noise
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10) [5/2/19] Signal detection — locally optimum coherent detection, coherent detection in general Gaussian noise
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11) [7/2/19] Signal detection — signals with random parameters, envelope detector
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12) [12/2/19] Signal detection — performance analysis of the envelope detector
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13) [14/2/19] Signal detection — completely random signals, energy detector
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14) [19/2/19] Sequential detection
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15) [26/2/19] Sequential detection — SPRTs and Wald’s approximations
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16) [7/3/19] Performance analysis of detectors — Chernoff bounds
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17) [9/3/19] Introduction to estimation, Method of moments estimators
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18) [12/3/19] Maximum likelihood estimators, Bayes estimators
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19) [14/3/19] Mean-square error for estimators, Best unbiased estimators
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20) [26/3/19] Cramer-Rao Lower bound for unbiased estimation
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21) [28/3/19] Sufficient statistics
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22) [30/3/19] Minimal sufficient statistics
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23) [2/4/19] Rao-Blackwell theorem, Complete statistics, Lehmann-Scheffe theorem
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24) [4/4/19] Asymptotic performance — consistency and asymptotic efficiency of MLEs
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25) [6/4/19] General decision theory framework for estimators, conditional expectation as the optimal MMSE estimator
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26) [9/4/19] State estimation in linear dynamical systems, Kalman-Bucy filter
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27) [11/4/19] Kalman-Bucy filter, Linear MMSE estimation theory
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28) [13/4/19] Yule-Walker equations, Levinson-Durbin filter
Last updated: 28-Jul-2024, 23:23:53 IST