[SciPy-user] computing Bayesian credible intervals
Damian Eads
eads@soe.ucsc....
Mon May 5 17:27:31 CDT 2008
Johann Cohen-Tanugi wrote:
> Hello,
> The question is a bit more general than that : How can I use SciPy to
> compute the values a and b defined by :
> 1) integral from a to b of a pdf p(x) (or any function for that matter)
> = a given value q
> 2) p(a)=p(b)
>
> thanks in advance,
> Johann
Computing the area of the posterior over a credible interval involves
integration. If your prior and likelihood are conjugate, it might be
easier to use a conjugate distribution parameterized with the posterior
hyperparameters and then compute CDF(b)-CDF(a). See
http://en.wikipedia.org/wiki/Conjugate_prior for a list of conjugate
priors with the hyperparameters worked out.
Now, I guess what your really asking is how to do the inverse of that
(question #1), i.e. how do you find the end points of the interval if
you know the area? Try the inverse CDF or inverse survival function. In
Scipy, some distributions have an isf member function.
b=post.isf(q)
a=0.0
Now onto question #2, let's assume your posterior distribution is
symmetric, you can try the inverse CDF or the inverse survival function.
For example, if q=0.7 (70%) and the posterior is symmetric, then
L=[post.isf(0.85), post.isf(0.15)]
a=min(L)
b=max(L)
Note, post.pdf(a) should be equal to post.pdf(b) because post is symmetric.
Cheers,
Damian Eads
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