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POProperly evaluating double integral in python
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  1. POProperly evaluating double integral in python
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    copied!<p>I am trying to compute a definite double integral using scipy. The integrand is a bit complicated, as it contains some probability distributions to give weight to how likely is each value of x and y (like a mixture model). The following code evaluated to a negative number, but it should be bound by [0,1]. Additionally, it took about half an hour to compute. </p> <p>I have two questions. </p> <p>1) Is there a better way to calculate this integral? </p> <p>2) Where is this negative value coming from? The big question for me is how to speed the calculation up, as I can find the bug in my code that's leading to the negative later on my own.</p> <pre><code>from scipy import stats from scipy.integrate import dblquad import itertools p= [list whose entries are each different stats.beta(a,b) distributions] def integrand(x,y): delta=x-y marg=0 for distA,distB in itertools.permutations(p,2): first=distA.pdf(x) second=distB.pdf(y) weight1=0 weight2=0 for distC in p: if distC == distA: continue w1=distC.cdf(x)-distC.cdf(y) if weight1 == 0: weight1=w1 else: weight1=weight1*w1 marg+=(first*weight1*second) I=delta*marg return I expect=dblquad(integrand,0,1,lambda x: 0, lambda x: x) </code></pre> <p>This is asking essentially what for the expected value of the maximal distance between two points is in a vector of distributions. The limits of integration are y ∊ [0,x] and x ∊ [0,1]. This gave me about -.49, with an estimated error of the integral on the order of 10e-10, so it shouldn't be due to the integration method.</p> <p>I've been fighting with this for a while and appreciate any help. Thanks.</p> <p>edit: corrected typo</p>
 

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