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Understanding
Bayes’Theorem
By David Siegel
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 li...
You test positive.
What is the likelihood 

that you have the disease?
Here is the problem:
Please work out your answer be...
People
who have
the
disease:
1%
A priori:
True
positives:
1% * 98%
False
positives:
2%
False negatives
Test accuracy: 98%
1% * 2%
After testing everyone:
True
positives:
980
False negatives:
Total population:
100,000
20
False
positives:
2,000
It helps to use numbers:
Chance you
have nose
cancer
True positives
=
All positives
Given that you tested positive:
Chance you
have nose
cancer
True positives
=
All positives
This is Bayes’Theorem!
Chance you
have nose
cancer
980
=
980 + 2,000
Plug in the numbers:
Chance you
have nose
cancer
980
=
2,980
= 32.88%
Do the math:
33%!
Chances that you have nose
cancer, given that you tested
positive:
Before test
1%
After test
33%
This is called a Bayesian update:
update
What if your test had
been negative?
What is the chance you
have nose cancer now?
Extra-credit question:
Understanding
Bayes’Theorem
Learn more at www.businessagilityworkshop.com
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Understanding bayes theorem

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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:
  14. 14. Understanding Bayes’Theorem Learn more at www.businessagilityworkshop.com

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