[SciPy-user] computing Bayesian credible intervals : help on constrained optimisation schemes?
Mon May 5 08:37:51 CDT 2008
I am attaching my script. I followed Neil's suggestion but it fails to
converge, due seemingly to issues with the fact that a and b must be
positive, which I cannot enforce with fsolve, AFAIK.
I am ready to dive into constrained schemes, especially in openOpt, but
I was hoping for some suggestions beforehand as to which path to follow
to solve this problem now.
I remind that I am trying to find a and b so that :
integral from a to b of p(x) = Q
where Q is given (0.95 in my script) and p is a Poisson posterior pdf
for ON/OFF source experiments. a,b, and x are source rates, and as such
People will have recognized the computation of a Bayesian credible
thanks a lot in advance,
Neil Martinsen-Burrell wrote:
> Johann Cohen-Tanugi <cohen <at> slac.stanford.edu> writes:
>> hi Neil, thanks for your answer and sorry I was not clear enough. Of
>> course I require the 2 conditions. 1) defines *a* credible interval if p
>> is a posterior pdf; and 2) sets a constraint that for common situation
>> yield *the* standard Bayesian credible interval. I will have a look at
>> brentq, I do not know what it refers to.
> scipy.optimize.brentq is Brent's method for finding a root of a given scalar
> equation. Since you are looking for two values, a and b, with two conditions,
> then Brent's method is not appropriate (barring some symmetry-based reduction to
> one variable). I like to use scipy.optimize.fsolve to find roots of
> multivariable equations, such as
> def solve_me(x): # x is an array of the values you are solving for
> a,b = x
> integral_error = quad(density, a , b) - q
> prob_difference = density(b) - density(a)
> return np.array([integral_error, prob_difference])
> fsolve(solve_me, [0.0, 1.0]) # initial guess is a = 0, b = 1
> SciPy-user mailing list
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