Learning Outcomes
The course aims to expose students and help them comprehend:
1. The problem of estimation and its applications
2. The various estimator structures and their properties
3. The problem of detection and its applications
4. The hypothesis tasting (formulation and solution)
5. The various methods of deterministic and stochastic signal detection
Course Content (Syllabus)
Estimation theory:
General Minimum Variance Unbiased Estimation
Cramer-Rao lower bound
Minimum Variance Unbiased Estimation of linear model parameters
Best linear unbiased estimator
Maximum likelihood estimators
Least squares estimators
Bayes estimator
Wiener filter
Kalman filter
Theory of detection:
Theory of statistical decisions.
Hypothesis testing and the Neyman – Pearson theorem
Hypothesis testing via Bayes risk minimization
ROCs
Detection of deterministic signals in noise, the matched filter.
Detection of random signals in noise
Course Bibliography (Eudoxus)
- Στατιστική Επεξεργασία Σημάτων και Μάθηση. Δημήτρης Αμπελιώτης, Χρήστος Μαυροκεφαλίδης, Κώστας Μπερμπερίδης, ΕΛΛΗΝΙΚΑ ΑΚΑΔΗΜΑΪΚΑ ΗΛΕΚΤΡΟΝΙΚΑ ΣΥΓΓΡΑΜΜΑΤΑ ΚΑΙ ΒΟΗΘΗΜΑΤΑ, 2015
Additional bibliography for study
1α. Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory, by Steven M. Kay, Prentice Hall, 1993
1β. Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory, by Steven M. Kay, Prentice Hall 1998.
2. Statistical Inference for Engineers and Data Scientists, by Pierre Moulin and Venugopal V. Veeravalli, Cambridge University Press, 2019