How to integrate a multidimensional normal density of 6 dimensions

Hello,

I'm a bit new in the field so I'm not sure my question has an answer.

I have dataset of 6 dimensions and I want to infer to probability distribution from it. I would like, at some point of the process, to quantize my function as, at the end I would need the pmf (probability mass function).

My approach was to assume multivariate normal distribution.

In a first step I quantize my dataset, cutting each dimension into bins of variable widths. Then I take the original dataset and infer the multidimensional probability distribution with the mvnpdf function. In the last step I would like, then, to approximate

Pr(X1,X2,X3,X4,X5,X6) = sum_{bin1}sum_{bin2}....sum_{bin6}f(x1,x2,x3,x4,x5,x6)dx1dx2dx3dx4dx5dx6 /(len(bin1)*...*len(bin6))

With binJ being the bin containing the value XJ in dimension J

Someone has an idea about how to make a 6-d integration ? Or propose another solution to deal with this problem ?

I already studied some other possibilities but I didn't find any suiting my problem

If someone can help it's a bit urgent

Thanks

Hadrien

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/29922-why-your-question-is-not-urgent-or-an-emergency

Answer 1

[Shashank Prasanna]

If you are looking to fit a distribution to your data then you can directly use the FITDIST function by specifying the distribution:

http://www.mathworks.com/help/stats/fitdist.html

Since you know you want a multivariate normal distribution you could directly use:

http://www.mathworks.com/help/stats/normfit.html

Answer 2

[Hadrien]

First of all thanks a lot for your fast answer

My problem is not so much to fit the multivariate normal distribution to my data but to quantize my data and fit a discrete distribution on this discretized (quantized) dataset

I have

Dataset = [X11 X12.... X16;

        X21X22......
        ............
        Xn1      Xn6]

I quantize it defining bins for each dimension, each value falling in a bin is assigned the same value so I obtain

Quantize = [Q11 Q12.... Q16

        Q21Q22......

        ............

        Qn1      Qn6]

With Qij being the value of the bin in which the dimension j of sample i falls

And then define the probability of P(Qi1,Qi2,..,Qi6)