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: NeymanPearson detectors

5

Framework, decision rules, classifying tests, testing of binary hypotheses

6

NeymanPearson lemma, ROC curves, sufficiency in hypothesis testing

7

Composite binary hypotheses, UMP tests, KarlinRubin 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,
continuoustime hypotheses

Minimum variance unbiased estimation/Maximum likelihood
estimation

12

MVUB estimators, BLU estimators, CramerRao 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, GaussMarkov theorem, linear statistical model, sequential
Bayes

Minimum meansquared 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
