← All Books

Statistical Inference, Detection & Estimation

From Detection Theory to Compressed Sensing and AMP

Statistical inference from classical detection and estimation through modern high-dimensional methods: sparse recovery, message passing, random matrix theory, and information-theoretic limits.

25 chapters206 sections88+ hours of content
Start from Chapter 1

Chapter Dependency Map

Click a chapter to see details, click again to open. Drag to rearrange.

Detection TheoryParameter EstimationHigh-Dimensional Estimation and Compressed SensingHigh-Dimensional Statistics and Sparse RecoveryAdvanced Topics in EstimationFrontiers of Statistical InferenceFuture topics

All Chapters

Part 1: Hypothesis Testing and Detection

Chapter 1

Binary Hypothesis Testing

~210 minFoundational
Chapter 2

Detection in Gaussian Noise

~210 minIntermediate
Chapter 3

M-ary Hypothesis Testing

~210 minIntermediate
Chapter 4

Sequential Detection and CFAR

~180 minIntermediate

Part 2: Parameter Estimation

Chapter 5

Estimation Theory Fundamentals

~210 minIntermediate
Chapter 6

Maximum Likelihood Estimation

~200 minIntermediate
Chapter 7

Bayesian Estimation

~180 minIntermediate
Chapter 8

The EM Algorithm and Iterative Estimation

~210 minIntermediate

Part 3: Linear Estimation and Filtering

Chapter 9

The Discrete-Time Wiener Filter

~180 minAdvanced
Chapter 10

The Kalman Filter

~220 minAdvanced
Chapter 11

Equalization as Inference

~160 minIntermediate
Chapter 12

MIMO Detection

~200 minAdvanced
Chapter 13

Sparsity and the ℓ1\ell_1 Relaxation

~200 minAdvanced

Part 4: Sparse Estimation and Compressed Sensing

Chapter 14

Algorithms for Sparse Recovery

~210 minAdvanced
Chapter 15

Compressed Sensing for Communications

~200 minResearch
Chapter 16

Random Matrix Theory for Estimation

~240 minAdvanced

Part 5: Graphical Models and Message Passing

Chapter 17

Factor Graphs

~180 minIntermediate
Chapter 18

Belief Propagation — The Sum-Product Algorithm

~280 minAdvanced
Chapter 19

Turbo Principle and Iterative Receivers

~240 minAdvanced
Chapter 20

Approximate Message Passing (AMP)

~220 minAdvanced
Chapter 21

OAMP, VAMP, and Beyond

~240 minResearch
Chapter 24

Information-Theoretic Bounds for Estimation

~240 minResearch

Part 6: Advanced Topics and Research Frontiers

Chapter 22

High-Dimensional Estimation

~220 minAdvanced
Chapter 23

Robust and Non-Parametric Estimation

~220 minAdvanced
Chapter 25

Open Problems and Connections

~200 minResearch