**ECE 561: Statistical Inference for Engineers and Data Scientists**

SPRING 2023

## Course Information

**Class time and place: **11:00 - 12:20 TR, 2013 ECEB
**Instructor: ** Prof. Pierre Moulin 310 CSL (pmoulin@illinois.edu)

Office Hours: Wednesdays 10:15 - 11:45 am in 310 CSL
**Teaching Assistant: **Weichao Mao (weichao2@illinois.edu)

Office hours: Tuesdays 4 - 6 pm in 3034 ECEB
- Syllabus
- Gradescope course entrycode: 3J27N4
**Required Text: **P. Moulin and V. V. Veeravalli, Statistical Inference for Engineers and Data Scientists, 2019
**Grading: **10% Homework, 25% Exam 1, 25% Exam 2, 40% Final exam
**References: **A number of references are on reserve in the Engineering Library, including books by T. S. Ferguson, J. O. Berger, E. L. Lehmann (2), S. M. Kay (2), B. C. Levy, H. V. Poor, and H. L. Van Trees

## Outline

- Elements of Statistical Decision Theory (Ch. 1): a general framework for discussing the Bayes and minimax approaches to detection and estimation; M-ary hypothesis testing and Bayesian parameter estimation obtained as special cases.
- Hypothesis Testing (Ch. 2, 3, 4): Bayesian decision rules; Minimax decision rules; Neyman-Pearson decision rules (the radar problem); composite hypothesis testing.
- Signal Detection in Discrete Time (Ch. 5): models and detector structures; performance evaluation.
- Convex Statistical Distances (Ch. 6): f-divergences and Ali-Silvey distances; bounds on classification error.
- Chernoff Bounds and Large Deviations (Ch. 7,8): Chernoff divergences, Bhattacharyya distances, Kullback-Leibler divergence, large-deviations analysis, application to hypothesis testing.
- Parameter Estimation (Ch. 11-14): Bayesian estimation; nonrandom parameter estimation; Cramer-Rao bounds; maximum likelihood estimation; asymptotic optimality; M-estimators.
- Additional Topics: Robust detection and estimation.

## Homework

- Homework 1: Problems 1.3, 1.5, 1.7, and 2.2 from course textbook. Due Thursday Feb. 2, 5pm on Gradescope.