Course breakdown on a per-lecture basis
| General
|
| 1
|
Introduction, elements of matrix algebra (quadratic forms,
Gram determinant)
|
| 2
|
Elements of matrix algebra (differentiation, orthogonal matrices, QR
factorisation, SVD, projections and rotations
|
| 3
|
Optimisation, multivariate methods, principal components
|
| 4
|
Sufficiency
|
|
Hypothesis testing: Neyman-Pearson detectors
|
| 5
|
Framework, decision rules, classifying tests, testing of binary hypotheses
|
| 6
|
Neyman-Pearson lemma, ROC curves, sufficiency in hypothesis testing
|
| 7
|
Composite binary hypotheses, UMP tests, Karlin-Rubin theorem
|
| 8
|
Invariance, UMP invariant tests
|
| 9
|
Matched filters, CFAR matched filters, locally most powerful tests
|
|
Hypothesis testing: Bayes detectors
|
| 10
|
Risk, Simple binary hypothesis Bayes detector
|
| 11
|
General formulation, likelihood ratios and posterior probabilities,
continuous-time hypotheses
|
|
Minimum variance unbiased estimation/Maximum likelihood
estimation
|
| 12
|
MVUB estimators, BLU estimators, Cramer-Rao lower bound
|
| 13
|
Efficient estimators, ML estimation, asymptotic properties, sufficiency,
invariance
|
|
Bayes estimators
|
| 14
|
Bayes risk, minimax estimators, computing Bayes estimators, Bayes
sufficiency and conjugate priors
|
| 15
|
MVN model, Gauss-Markov theorem, linear statistical model, sequential
Bayes
|
|
Minimum mean-squared error estimation
|
| 16
|
Conditional expectation and orthogonality, MMSE and LMMSE estimators,
linear prediction
|
| 17
|
Kalman filtering
|
|
Least Squares
|
| 18
|
Linear model, least squares solution, performance, weighted LS
|
| 19
|
Constrained LS, underdetermined LS, structured correlation matrices
|
|
Conclusion
|
| 20
|
Overview of principles and techniques
|
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