Question:Evaluating multi-variable integration

Question:Evaluating multi-variable integration

Maple 14

Hi everyone,

In my research project, I needed to evaluate a multi-variable integration. I'm trying to do this in Maple, and seems no matter I use Int or int, it failed to evaluate the integration.

Here's my code:

I'm integrating a joint probability density function which is basically a multiplication of four PDFs of four Gaussian distributions:

` `
`> mu := 0:                                                                                                            `
`> sigma := 0.25:                                                                                                      `
`> elist := [e1, e2, e3, e4]:                                                                                  `
`> E := Statistics:-RandomVariable(Normal(mu, sigma)):             `
`                                                    > jointPDF := product(Statistics:-PDF(E, elist[i]), i = 1..4):`
` `
`> jointPDF;                                       2                     2                     2                     2        64.00000000 exp(-8.000000000 e1 ) exp(-8.000000000 e2 ) exp(-8.000000000 e3 ) exp(-8.000000000 e4 )        ---------------------------------------------------------------------------------------------------                                                          2                                                        Pi`

The integration area is:

` `
`> area := [e1 = e4 - 1.800000000 .. infinity, e4 = e2 + 0.900000000 .. infinity, `
`e2 = e3 - 1.800000000 .. infinity, e3 = -infinity .. infinity]:`
` `

I tried both of the numerical and the symbolic ways:

` `
`evalf(Int(jointPDF, area)) `
` `

and

` `
`evalf(int(jointPDF, area))`
` `

The second one executes for a long time, and returns an unevaluated integration expression. The first command immediately gives back the unevaluated expression. Also I'm wondering is it possible to use Monte Carlo method to evaluate this integration?

`Any suggestion on evaluating this integration is appreciated. Thanks!`
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