Introduction and Guiding Examples

This is an introductory chapter where two general problems in high-dimensional testing and inference are introduced. Namely, the signal detection and signal support estimation problems. This is done in the context of two general models—the signal-plus-noise model and the chi-square model arising in genome-wide association studies. Motivating applications of these two problems and two models are briefly discussed. The chapter concludes with a summary of the contents of the manuscript.