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January 11th, 2014, 07:08 PM  #1 
Newbie Joined: Jan 2014 Posts: 1 Thanks: 0  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. 
January 12th, 2014, 12:31 AM  #2 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  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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