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Jul
12
comment Performance of numerical optimization with triple integral
Your solution is very clear and runs swiftly.
Jul
12
comment Performance of numerical optimization with triple integral
Thanks for this. I've changed the question again so that it is framed around the non trivial problem, and not implying directly a solution related to a change in coordinates. I'm not very experienced with the forum, so I hope this structure makes more sense to everyone (I suppose that's why it was put on hold as off topic)
Jul
12
revised Performance of numerical optimization with triple integral
Improved wording and phrasing of the actual question
Jul
11
revised Performance of numerical optimization with triple integral
added 95 characters in body
Jul
11
comment Performance of numerical optimization with triple integral
I've edited the question to allow for a non-trivial optimization (and have already included some of your suggestions). Any further advances to solve such a problem would be much appreciated
Jul
11
revised Performance of numerical optimization with triple integral
Additional information
Jul
11
comment Performance of numerical optimization with triple integral
If you call the function with any explicit argument, say q2[1,1] you get an error message. Do you know what that is? I think that something is going on with it, but NMaximize is not picking it up because in this simplified version of the problem there is only one feasible point...
Jul
11
comment Performance of numerical optimization with triple integral
Thanks. Yes, I do realize the constraint makes the problem trivial, but I was just trying to make a small tractable version of my problem to ask the question. Having said that, your point is relevant - and I hadn't realized that using CDFs (actually I need to use SurvivalFunction because my actual distributions are not symmetric) significantly improves performance.
Jul
10
awarded  Commentator
Jul
10
comment Performance of numerical optimization with triple integral
Thanks. I'm trying to compile it but get an error. A couple of questions, just to check I understand what is going on: (1) there is a square bracket missing at the end of the definition of q2 (i.e. at the end of NIntegrate)...right? (2) What is jd?
Jul
10
revised Performance of numerical optimization with triple integral
Typo
Jul
10
comment Speed of convergence for NIntegrate
Here is a more detailed exposition of the problem I'm trying to solve. Thanks
Jul
10
asked Performance of numerical optimization with triple integral
Jul
10
accepted Speed of convergence for NIntegrate
Jul
10
comment Speed of convergence for NIntegrate
Interesting approach. However it turns out that performance is indeed crucial because the problem I actually want to solve is a non-linear constrained optimisation problem over the limits of the integral. I tried transforming the integrand as you suggest (i.e. shifting the peak as a function of the truncation points) but this does not improve performance sufficiently. Your last suggestion is hence relevant. I don't know how to transform the problem to shperical coordinates, so I'll try -and probably open a new post asking about it. Thanks!
Jul
9
comment Speed of convergence for NIntegrate
Thanks. Increasing working precision alone does get rid of the message but does not seem to improve the time significantly (at least once you embed it in a more complicated numerical optimisation routine). I'll try the two strategies you mention, and will def read the tutorial on integration strategies
Jul
9
asked Speed of convergence for NIntegrate
Mar
26
comment Empirical Cumulative Distribution Function
I accepted kirma's answer because it came first and gives an exact solution. I however upvoted your answer because it is a useful approximation (and works directly with Mathematica 8). Thanks!
Mar
26
comment Empirical Cumulative Distribution Function
@kirma Thanks. Very useful (works alright with Mathematica 8 as you suggest). Yes, I am dealing with empirical data, so I don't know exactly the data generating process and would hence prefer not to impose any parametric assumptions (and some of my other plots seem to fit less neatly normal distributions).
Mar
26
accepted Empirical Cumulative Distribution Function