The math behind Bayes' Theorem clearly explained!

🧵

In this 🧵 We will calculate with the numbers from the disease example.

You can find the example here:




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For better understanding, we will create a contingency table with our numbers:

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We want to know:

What is the probability that you have the disease given that you have tested positive?

Mathematically,

P(A | B) = P(You have disease | Tested positive)

So

A = sick

B = tested positive

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Now let's do the math.

1. Calculate P(A) namely the probability of being sick, this is our first prior.

Note: we can calculate this from the table, or from the given information:

We know that 1 out of every 10,000 patients is sick.

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2. Calculate the other prior P(B), namely the probability of being tested sick.

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3. Now calculate the event.

Our event is P(B | A), so being tested sick, when you are sick.

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Now we can put everything together 🔽

The probability of being sick when you are tested sick is less than 1%.

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That's it for today.

I hope you've found this thread helpful.

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Thanks

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