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# Understanding bayes theorem

This helps get you started on your journey to becoming Bayesian.

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### Understanding bayes theorem

1. 1. Understanding Bayes’Theorem By David Siegel
2. 2. 1 out of 100 people has nose cancer, a fictional disease 1 A new test is 98% accurate.2 You test positive.3 What is the likelihood   that you have the disease? 4 Nose cancer! Here is the problem:
3. 3. You test positive. What is the likelihood   that you have the disease? Here is the problem: Please work out your answer before continuing …
4. 4. People who have the disease: 1% A priori:
5. 5. True positives: 1% * 98% False positives: 2% False negatives Test accuracy: 98% 1% * 2% After testing everyone:
6. 6. True positives: 980 False negatives: Total population: 100,000 20 False positives: 2,000 It helps to use numbers:
7. 7. Chance you have nose cancer True positives = All positives Given that you tested positive:
8. 8. Chance you have nose cancer True positives = All positives This is Bayes’Theorem!
9. 9. Chance you have nose cancer 980 = 980 + 2,000 Plug in the numbers:
10. 10. Chance you have nose cancer 980 = 2,980 = 32.88% Do the math:
11. 11. 33%! Chances that you have nose cancer, given that you tested positive:
12. 12. Before test 1% After test 33% This is called a Bayesian update: update
13. 13. What if your test had been negative? What is the chance you have nose cancer now? Extra-credit question: