CS 8850 : Advanced Machine Learning Fall 2017 Topic 3 : Hypothesis Testing

Example 3.2 (Radar). A radar is constantly emitting a signal and monitoring to see if it bounces back (see Figure 3.1). The signal x that the radar receives can be modeled as N (0, σ) if there is nothing (hence the signal doesn’t bounce back) and N (μ, σ) for some μ > 0 if an object is present (hence signal bounces back). Thus it needs to decide between: H0 : x ∼ N (0, σ) ⇒ nothing there, H1 : x ∼ N (μ, σ), μ > 0 ⇒ something there.