Detection Theory Notes

Notes Covers the following topics:

- Max and min of two IID Random Variables (Page 01)
- Leibniz integral rule (Page 02)
- Bayesian Hypothesis testing (Page 03)
- Likelihood ratio test (Page 05)
- Bayesian Hypothesis testing with Gaussian Error (Page 05.5)
- Probability of error and Minimax Hypothesis (Page 08.5)
- Minimax Detector (Page 09.5)
- Example: Gaussian error with non-uniform cost (Page 12)
- Bayesian vs Minimax vs Neyman-Pearson Hypothesis (Page 14)
- Neyman-Pearson Hypothesis (Page 14.5)
- Intuition from Neyman-Pearson Hypothesis (Page 15.5)
- Receiver Operating Characteristic (ROC) (Page 16.5)
- Example: Bayesian Decision Rule in Binary Channel (Page 17)
- Example: Bayesian Rule, Minimax Rule and Neyman-Pearson Rule Calculation (Page 18.5)
- Composite Hypothesis Testing (Page 21.5)
- Uniformly Most Powerful test (UMP test) (Page 24.5) 
- Signal Detection (Page 25.5)
- Detection of the Deterministic Signals (Coherent Detection) (Page 26.5)
- Detection of Deterministic Signals in Gaussian Noise (Page 27.5)
- Deterministic of Non-coherent Signals (Modulated Signal Carrier) (Page 28.5)
- Chernoff & Related Bounds (Page 30)
- Bhattacharyya Bound (Page 31)
- Bhattacharyya Distance and Bhattacharyya Coefficient (Page 31.5)
- Intuition from Bhattacharyya Bound (Page 32)
- Error Exponent (Page 33)
- Chernoff Bound for Location testing in Gaussian Noise (Page 33.5)
- Multiple Hypothesis Testing (M-ary hypothesis) (Page 35.5)
- Orthogonal Signal Detection (Page 37.5)
- Nonparametric and Robust Detection (Page 40.5)
- The Sign test (Non-parametric Detection) (Page 41)
- Example: The Sign test (Page 43.5)
- Robust Detection (Page 44.5)

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