Maximum Likelihood Estimation (MLE): Exact and approximate methods (EM algorithm, alternating maximization, etc.)Cramer-Rao Lower Bound (CRLB) Minimum Variance Unbiased Estimation (MVUE) Sufficient Statistics Best Linear Unbiased Estimation (BLUE) Large and Small Sample Properties of Estimators: Understanding the behavior of estimators in both large and small sample sizes Bayesian Inference and Estimation: Minimum Mean Square Error (MMSE) estimation MAP Estimation (Maximum A Posteriori Estimation)Wiener and Kalman Filtering (Sequential Bayes) Detection Theory: Likelihood Ratio Testing Bayes Detectors Minimax Detectors Multiple Hypothesis Tests Neyman-Pearson Detectors (Matched Filter, Estimator-Correlator, etc.) Wald's Sequential Test Generalized Likelihood Ratio Tests (GLRTs) Wald and Rao Scoring Tests

Same as Reference

1. Fundamentals of Statistical Signal Processing: Estimation Theory (Vol1), Detection Theory (Vol2), M. Kay's, Prentice-Hall Signal Processing Series, 1993.

2. Linear Estimation, Kailath, Sayed and Hassibi, Prentice-Hall Information and Sciences Series, 1st edition, 2000.

3. Statistical Signal Processing (Paperback) by LouisScharf,1st edition.

4. An Introduction to Signal Detection and Estimation, Poor, H. Vincent, Springer Text in Electrical Engineering,1994.

5. Detection, Estimation, and Modulation Theory –Part I,H.Van Trees,et.al,2nd edition, Wiley.

6. Monte Carlo Strategies in Scientific Computing, J.S.Liu, Springer‐Verlag, 2001.

7. Stochastic Simulation, B.D.Ripley, Wiley, 1987.

Course Outcomes (COs):

CO1: Understand various methods of statistical inferencing, namely, estimation and detection techniques

CO2: Ability to apply those methods for solving real life problems - both engineering and otherwise.

CO3: Design and Implementation of various algorithms for various problems using standard simulation tools such as Matlab, python etc.

CO4: Provide a platform for more advanced methods and algorithms from machine and deep learning.