Understanding bayes theorem

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Understanding Bayes’ Theorem By David Siegel

Transcript of Understanding bayes theorem

Page 1: Understanding bayes theorem

Understanding Bayes’ Theorem

By David Siegel

Page 2: Understanding bayes theorem

1 out of 100 people has nose cancer, a fictional disease

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A new test is 98% accurate.2

You test positive. 3

What is the likelihood that you have the disease?

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Nose cancer!

Here is the problem:

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You test positive.

What is the likelihood that you have the disease?

Here is the problem:

Please work out your answer before continuing …

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People who have the disease: 1%

A priori:

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True positives: 1% * 98%

False positives: 2%

False negatives

Test accuracy: 98%

1% * 2%

After testing everyone:

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True positives: 980

False negatives:

Total population: 100,000

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False positives: 2,000

It helps to use numbers:

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Chance you have nose cancer

True positives=

All positives

Given that you tested positive:

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Chance you have nose cancer

True positives=

All positives

This is Bayes’ Theorem!

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Chance you have nose cancer

980=

980 + 2,000

Plug in the numbers:

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Chance you have nose cancer

980=

2,980= 32.88%

Do the math:

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33%!

Chances that you have nose cancer, given that you tested positive:

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Before test1%

After test33%

This is called a Bayesian update:

update

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What if your test had been negative?

What is the chance you have nose cancer now?

Extra-credit question:

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Understanding Bayes’ Theorem

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