Lecture 9 - Hypothesis Testing

First part of EDC - Compendium.pdf, Ch 2.

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Hypothesis testing is a statistical process where you test an assumption (hypothesis) about a population parameter. If the evidence from the sample data strongly contradicts the hypothesis, you reject it in favor of an alternative hypothesis; otherwise, you fail to reject it.

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Terms

Binary Hypothesis Decision Regions Detector Confusion Matrix for Hypothesis Testing Receiver Operating Characteristics Multiple-Hypotheses Testing

Examples

Example 1 - Change in Mean Detection

Based on this, can we declare if we are in ${\mathcal{H}}_0$ or ${\mathcal{H}}_1$? Note, the PDF is given in terms of Bayesian Estimation

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Solution Since $\sigma$ is equal in both cases, we can use a simple solution like a threshold, and can in this case be the detector.

Example 2 - Change in Variance Detection

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Solution: We find the probabilities of both $f_0$ and $f_1$ in a point, and choose the pdf with highest probability (threshold, like we did earlier).