Lecture 10 - Neyman-Pearson and Bayesian Detectors

A more formal way of representing a Detector.

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There are two main approaches

• Classical approach - Neyman-Pearson Theorem
  • Detecting a constant signal in noise
• Bayesian approach - Bayesian Detection

Terms and Sub-Topics

Decision Regions Power of Test Size of Test Receiver Operating Characteristics

Main Idea

We want to find

[!Binary Case] ${\Omega }^{\ast }=arg{\min }_{\Omega }{\int }_{\Omega }g(x)dx$ ${\Omega }^{\ast }=\{x\in {\mathbb{R}}^N:g(x)<0\}$

M-ary case

$\{{\Omega }_1^{\ast },\dots ,{\Omega }_M^{\ast }\}=arg{\min }_{{\Omega }_1,\dots ,{\Omega }_M}{\sum }_{i=1}^M{\int }_{{\Omega }_i}{g}_i(x)dx$ ${\Omega }_1^{\ast }=\{x\in {\mathbb{R}}^N:g_i(x)<g_k(x),\forall k\ne i\}$

Which is the domains such that they only contribute negatively.