Chapter 1: Binary Hypothesis Testing

Learning Objectives

• Formulate a binary decision problem with priors, likelihoods, and a cost matrix
• Derive the Bayes-optimal decision rule and the MAP rule as its 0-1-cost special case
• Prove and apply the Neyman-Pearson lemma via the variational argument
• Read and construct a receiver operating characteristic (ROC) curve and interpret its concavity
• Derive the Bhattacharyya and Chernoff bounds on error probability and compute Chernoff exponents
• Apply LRT-based detection to binary signaling in additive Gaussian noise