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I am reading Nate Silver's book "The Signal and the Noise" and have a question about Bayes Theorem. I've created my own example and am trying to wrap my mind around the conclusion.

Let's say, before any information, I think there is a 5% chance humans have caused global warming.

Then, I hear information that scientists think there is a 99% chance that humans have caused global warming.

I also know that the probability that the 99% claim is wrong is 10%.

Using the Bayes Theorem calculation, the result is a 34% chance that humans cause global warming.

Here is the calculation:

X = initial probability of humans causing global warming = 5%

Y = probability of humans causing global warming, given scientist evidence = 99%

Z = probability of humans not causing global warming, given scientist evidence = 10%

The formula presented in the book (page 247) is:

Revised probability (given the new information) = XY / (XY + Z(1-X))

Revised probability (given the new information) = 34%


My intuition says that, after this new knowledge, the chances that humans have caused global warming is instead (10% * 1%) + (90% * 99%) or 90%.

This would be based on the fact that theres a 10% they're wrong and 90% chance they're right.


What is wrong about my application of the theorem or understanding of the theorem that causes this mental roadblock?

Thanks.

  • 0
    Perhaps you could tell how you calculated 33%2012-10-29
  • 0
    @Henry Just added the formula to the original question2012-10-29
  • 0
    Here is what I've come up with for why my logic is faulty: Bayes Theorem applies when there is an observable chance something happens, before new information, and after new information. My use of the theorem is based on a persons assumed % chance of truth, even though there is no evidence to suggest that the 5% number was correct.2012-10-29

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