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Math Help - Estimate probability of success given k successes in n trials

  1. #1
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    Estimate probability of success given k successes in n trials

    I'm trying to estimate the probability of success when I'm given data where a certain number of successes (k) occur in a certain number of trials (n).

    IOW, instead of trying to figure out the chances of k successes given n trials and a probability (p) (whcih I know how to do). I'm trying to estimate p when given k successes and n trials. An important note is that all potential values for p between 0 and 1 are equally likely.

    I can't seem to wrap my head around all of the Bayesian inference stuff I'm reading. I understand exactly what needs to be done involving the integral calculus, I just can't do it. Integration by parts just seems to lead to a never ending process.

    Any help?
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  2. #2
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    Quote Originally Posted by Capt Vee View Post
    I'm trying to estimate the probability of success when I'm given data where a certain number of successes (k) occur in a certain number of trials (n).

    IOW, instead of trying to figure out the chances of k successes given n trials and a probability (p) (whcih I know how to do). I'm trying to estimate p when given k successes and n trials. An important note is that all potential values for p between 0 and 1 are equally likely.

    I can't seem to wrap my head around all of the Bayesian inference stuff I'm reading. I understand exactly what needs to be done involving the integral calculus, I just can't do it. Integration by parts just seems to lead to a never ending process.

    Any help?
    Try Tabular Integration, near the bottom of this page: Integration by parts - Wikipedia, the free encyclopedia

    It speeds up things a lot!
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  3. #3
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    Quote Originally Posted by Capt Vee View Post
    I'm trying to estimate the probability of success when I'm given data where a certain number of successes (k) occur in a certain number of trials (n).

    IOW, instead of trying to figure out the chances of k successes given n trials and a probability (p) (whcih I know how to do). I'm trying to estimate p when given k successes and n trials. An important note is that all potential values for p between 0 and 1 are equally likely.

    I can't seem to wrap my head around all of the Bayesian inference stuff I'm reading. I understand exactly what needs to be done involving the integral calculus, I just can't do it. Integration by parts just seems to lead to a never ending process.

    Any help?
    Hi Capt Vee,

    I sounds like you want a Binomial proportion confidence interval. If you simply want a method for computing a confidence interval (rather than a derivation), you can find some methods described here:

    Binomial proportion confidence interval - Wikipedia, the free encyclopedia
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  4. #4
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    If this is a Bernoullit trial, try using the Binomial Model.
    If it is, let me know. I"ll elaborate.
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