# Thread: Understanding and Calculating Credible Intervals

1. ## Understanding and Calculating Credible Intervals

Hi,

I am having trouble understanding and calculating credible intervals. My goal is to understand confidence intervals vs. credible intervals.

From what I understand, the credible interval is a range of values (parameter?) that is fixed (not really) based on the prior probability distribution. I am assuming that the posterior probability distribution is the same as the prior probability distribution.

I found something that I am trying to understand about credible intervals,but I got a bit lost in the wording. Is there an equation that helps calculate credible intervals?

I am trying to decipher what the attachment means.

2. ## Re: Understanding and Calculating Credible Intervals

Originally Posted by bmac1
I am assuming that the posterior probability distribution is the same as the prior probability distribution.
Nope, they're different. I think the first thing to do here would be to try and get a good conceptual understanding of how confidence intervals and credible intervals differ (before moving on to calculations). This thread should get you started: https://stats.stackexchange.com/ques...dible-interval

3. ## Re: Understanding and Calculating Credible Intervals

Originally Posted by bmac1
I am assuming that the posterior probability distribution is the same as the prior probability distribution.
Originally Posted by CowboyBear
Nope, they're different.
My guess is that, in this very specific and extremely contrived example, OP is assuming the same function form between the prior and the posterior distribution? I mean, almost all introductory texts I've seen about Bayesian statistics take the classic "coin tossing" model example because the Beta distribution acts as a conjugate prior here.

But related to the specific question of:

Originally Posted by bmac1
Is there an equation that helps calculate credible intervals?
Most of the time the answer is "no". These things are complicated and usually need to be approximated via computer methods, unless you're dealing with an example that is so contrived and simple that you can actually work it out by hand.

4. ## Re: Understanding and Calculating Credible Intervals

Originally Posted by spunky
My guess is that, in this very specific and extremely contrived example, OP is assuming the same function form between the prior and the posterior distribution? I mean, almost all introductory texts I've seen about Bayesian statistics take the classic "coin tossing" model example because the Beta distribution acts as a conjugate prior here.

But related to the specific question of:

Most of the time the answer is "no". These things are complicated and usually need to be approximated via computer methods, unless you're dealing with an example that is so contrived and simple that you can actually work it out by hand.
I have read that stackexchange forum many times and still don't understand the jargon.
I think what I am having trouble with is how the prior, beta-binomial poster distribution, and the beta distribution fit in the credible interval?

I understand that you need to know what your prior distribution is before getting the credible interval.

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