I am trying to symbolically evaluate the expectation of a complicated multivariate random variable expression. The multivariate distribution is Gaussian which is easily (but abstractly) specified
It would help if you include the expression you are trying to evaluate, even in general form. Quite often we can evaluate Gaussian integrals of many variables analytically by diagonalising the quadratic term in the exponential. I would try that before resorting to such a software.
I think, that Maple is a best software for symbolic calculations (as far as I know, even MathCAD and Matlab use Maple engine for symbolic calculations).
I think, that Mathematica is the best software for symbolic calculation.
Raphael,
The quadratic terms in my exponential is actually diagonal so I have that advantage. The linear terms are however arbitrary. The problem is mainly in the polynomial whose expectation I want. This is the product of two double sums of cubic terms in the random variables. With laborious effort I succeeded in simplifying to a rather nice form involving the quadratic and linear coeficients for the exponential distribution but I really would like to make sure I haven't slipped up somewhere.
CoCoA-5 is a free Computer Algebra System. (I'm one of the authors ;-)
Expectation[
x^3 + 4 y - a z, {x, y, z} \[Distributed]
MultinomialDistribution[10, {1/2, 1/3, 1/6}]]
Here is an example similar your problem.
Further, more complicated examples follow.
Probability[x^2 > 12 \[Conditioned] x > 2,
x \[Distributed] PoissonDistribution[2]] in Mathematica gives you the prob of a conditional event.
An example for conditional expextation is Expectation[x^5 \[Conditioned] x > 2,
x \[Distributed] NormalDistribution[]]
How do you do it in Matlab or CoCoA???
I admit: I don't know the definition, I'm an algebraist...
But I'm a fairly good programmer too ;-) and CoCoA is free software: if you are interested and give me the definitions....
Hi Dr Kleeman,
I believe that the attached link is exactly what you are looking for. It will give you the exact expectation symbolically in terms of the mean and variance for the random variables. I am also attaching the relevant reference to the toolbox in the link.
Feel free to contact me should you require further information. I have MATLAB and Mathematica source codes to the toolbox.
My best wishes to you,
Arvind
http://aue.erc.monash.edu.au/webMathematica/Asue/MTMC.jsp
Article Analytical Standard Uncertainty Evaluation Using Mellin Transform
Article Standard uncertainty evaluation of multivariate polynomial
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