Detection, Estimation and Classification
Subject code: SIP 7012
Lecturer
Assoc. Prof. Anatoli Torokhti
University of South Australia
Mode of delivery
On-line only.
Assumed knowledge
A basic knowledge of probability theory and statistics.
Aims/Learning Objectives
On successful completion of this course, students will be able to:
- read the research literature on the subject;
- formulate a problem in detection, estimation and classification;
- implement algorithms in MATLAB to solve such a problem.
Thus the aim of the course is to understand the theory of this material and
to implement that understanding in the formulation and solution problems.
The examination at the end of the course will reflect this aim. Like
any worthwile course at this level, the underlying aim is to foster a
way of thinking about certain kinds of problems -- in this
case the handling of signals. This is not a recipe book, though students
will be provided with a collection of tools and ideas about where to use
those tools.
Content
Basic Ideas:
Probability - Probability distributions, expectations, multivariate normals;
Random variables; Independence; Conditional probability; Covariance matrix.
Hypothesis testing:
Bayes Rule; Likelihood; Applications to detection and classification problems;
Priors and MAP; Cost functions and decision rules; Minimum risk;
Composite testing:
ROC's; Kernel Estimator method for finding pdf.
Karhunen-Loeve and Linear Discriminate analysis:
Review of eigenvalues and eigenvectors, singular value decomposition;
Karhunen-Loeve method: reduction of continuous to discrete data;
Linear discriminant analysis; Linear detection; Linear classifier.
Parameter estimation:
Bias and consistency; Efficiency; Maximum Likelihood; Bayesian Estimates;
Linear Mean-Square Estimation.
Advanced parametric methods:
Minimax method; Neyman-Pearson method; The EM algorithm;
Robust parameter estimation and detection.
Evaluation:
Probability of error in hypothesis testing; Chernoff bounds;
Probability of error in parameter estimation; Cramer-Rao lower bounds;
Dimension and misclassification.
Assessment
50% examination, 50% assignments (5), essay (1), however these
percentages are indicative only and may be varied at the lecturer's discretion.
Details of the actual assessment used in a given year
can be found in the study guide provided at the start of the semester.
Resources
The notes cover all of the material students will be expected to know for
the course, but references to extension material will be provided too.