Thread: Definite integrals for Bayesian statistics

Hi,

As far as I know this has an analytical solution but I'm not sure how to go about doing it. Just to clarify, I'm not looking for a numerical method.

Sorry, don't know how to use maths symbols here:

I need to find x and y, such that the integral of exp(-ax^2 - b), evaluated from -infinity to x, equals 0.025, and the same integral evaluated from y to infinity equals 0.0975.

a and b are known constants.

(The question is just to find the 95% confidence interval from a posterior distribution).

Can anyone help?

Thanks!

Originally Posted by bsk

Hi,

As far as I know this has an analytical solution but I'm not sure how to go about doing it. Just to clarify, I'm not looking for a numerical method.

Sorry, don't know how to use maths symbols here:

I need to find x and y, such that the integral of exp(-ax^2 - b), evaluated from -infinity to x, equals 0.025, and the same integral evaluated from y to infinity equals 0.0975.

a and b are known constants.

(The question is just to find the 95% confidence interval from a posterior distribution).



Can anyone help?
Thanks!

up to some factors which you can pick out for instance take the out of the integrand and note that can be handled with the proper choice of , where is the square root of the variance of a normally distributed r.v., use the table for the normal distribution for answer.

Thanks, I think I've got it.

just be sure u scale things properly in the end, for there is the to consider, i.e., if X= is a normal r.v., then p(x), the probability density function of X is given by,


And thus