Detection and Estimation Theory
Graduate Course, IISc, 2022
Lecture notes consists of materials from my coursework both at IISc.
- Lec-1: Introduction
- Lec-2: Probability Review
- Lec-3: Binary Hypothesis Testing
- Lec-4: Bayesian Hypothesis Testing
- Lec-5: ML, MAP Detection & Operating Characteristics
- Lec-6: Minimax and Neyman-Pearson Testing
- Lec-7: Gaussian Hypothesis Testing
- Lec-8: Test with Discrete Observations
- Lec-9: Multiple Hypothesis Testing
- Lec-10: Intro to Composite Testing
- Lec-11: Composite Hypothesis Testing
- Lec-12: UMP Tests, Karlin-Rubin Theorem & GLRT
- Lec-13: Sequential Hypothesis Testing
- Lec-14: Sequential Hypothesis Testing Continued
- Lec-15: Intro to Estimation Theory
- Lec-16: MAP & MMSE Estimates
- Lec-17: MMSE properties
- Lec-18: Linear Least Squares Estimates (LLSE)
- Lec-19: Properities of LLSE
- Lec-20: LLSE: some examples
- Lec-21: Non-random Parameter Estimation
- Lec-22: Cramer-Rao Lower Bound
- Lec-23: Consistent and Efficient Estimators
- Lec-24: Sufficient Statistics & Neyman-Fisher Factorization
- Lec-25: Rao-Blackwell Theorem
- Lec-26: Best Linear Unbaised Estimates (BLUE)
- Lec-27: Gram-Schmidt Orthogonalization
- Lec-28: Kalman Filter
- Lec-29: Relation between Min-max and Bayesian testing
- Lec-30: Quickest Change-point Detection
- Lec-31: Convex Statistical Distances
- Lec-32: Ali-Silvey Distance
- Lec-33: Simple Lower Bounds and Chernoff Bounds
- Lec-34: Application of Chernoff Bounds
- Lec-35: Bounds on Classification error - coming soon
- Lec-36: Theory of Large Deviation - coming soon - coming soon