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January 11th, 2014, 07:08 PM   #1
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Problem of confidence in waiting, see details

Hi, I just registered for this problem. Any suggestions and thoughts will be helpful.

Scenario: I have an initial estimate of the probability of a specific event for each day, say P1. P1 is fairly small and I would like to know how good my estimation is. Specifically whether it should be smaller or not. So I start my observation for the event. After N days, the event did not occur. (The event itself is easily observed so no iffy observation.)

At this point, should I be confident that my initial estimation P1 should be smaller? Or the opposite, that I cannot conclude anything from my null observation?

Intuitively I would say one should lower the expectation after some null observation, but that's just intuition.
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January 12th, 2014, 12:31 AM   #2
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Re: Problem of confidence in waiting, see details

Try taking a look at this first.

http://en.wikipedia.org/wiki/Confidence_interval

In general, you need to calculate the probability of N null observations given your hypothesis of P1. If this probability is "too low" the you may reject your hypothesis in favour of a smaller P.
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