Multivariate mathematical statistics question

[noradetzky]

Under what conditions does:

 

\sigma_f=\sqrt{\left(\frac{\partial}{\partial x_1}f\sigma_{x_1}\right)^2+\left(\frac{\partial}{\partial x_2}f\sigma_{x_2}\right)^2+\ldots+\left(\frac{\partial}{\partial x_n}f\sigma_{x_n}\right)^2}

 

Hold true, where \sigma is error?

 

edit

 

Darn, I thought the TeX environment was integrated such that I didn't need to specify "\[\]" and stuff.

Edited March 25, 2012 by noradetzky

[John]

LaTeX is integrated with the forums. The way it works is you use [math] and [/math] around the LaTeX, like so:

 

[math]\sigma_f=\sqrt{\left(\frac{\partial}{\partial x_1}f\sigma_{x_1}\right)^2+\left(\frac{\partial}{\partial x_2}f\sigma_{x_2}\right)^2+\ldots+\left(\frac{\partial}{\partial x_n}f\sigma_{x_n}\right)^2}[/math]

 

Clicking on that will show the code used and a link to the SFN LaTeX tutorial.

Edited March 25, 2012 by John

[Xittenn]

Taking a stab at this, I believe what you are looking at is the error in position of a three dimensional object--this is probably relating back to HUP.

 

Or many dimensional . . .

 

But this would have to be for a vector product of some sort . . .

 

So like the error in vector displacement in n dimensions!

[timo]

It would certainly help if you could have been bothered to mention the context you have seen the equation in, and what the meaning of the symbols is, and what your scientific background is, ... . The keyword you are most likely looking for is "uncorrelated", followed by "small error".

Edited March 25, 2012 by timo

[Xittenn]

So like the uncorrelated small error in vector displacement over n dimensions!

 

 

How would you say this properly because now it neglects to say what is uncorrelated, which is the error of the components of the final vector . . .

[noradetzky]

It would certainly help if you could have been bothered to mention the context you have seen the equation in, and what the meaning of the symbols is, and what your scientific background is, ... . The keyword you are most likely looking for is "uncorrelated", followed by "small error".

 

The equation was presented to me as a simplified version of the delta method. I was confused since there were no covariances.

 

I have no scientific background. I am a first year undergraduate student in mathematics and statistics. I'm hoping to find research specialization in the stochastic process, but that's another question.

[Xittenn]

However poorly I've worded it this is simply an example of Propagation of Uncertainty. I guess I should review this as well because I'm obviously having trouble with the concept. The fact that these are uncorrelated means the final term for [math] (\frac{\sigma_f}{f})^2 [/math] is equal to zero because the vector uncertainties in combination with their respective vectors are orthogonal to all other vectors. The wiki on this is not the best either, try a year one physics book.

 

** there is also the partial derivative example below the general list . . .

 

[edit] changed to this "the vector uncertainties in combination with their respective vectors are orthogonal to all other vectors" from this "the vector uncertainties and their respective vectors are orthogonal to each other" because it sounded like the uncertainty was orthogonal to its respective vector which was not what I meant!

Edited March 26, 2012 by Xittenn

[timo]

The equation was presented to me as a simplified version of the delta method. I was confused since there were no covariances.

Covariances for uncorrelated statistical variables vanish.

 

I have no scientific background. I am a first year undergraduate student in mathematics and statistics.

Concerning a question about statistics that already is a stronger background than most of the people on this forum have. Many (most?) people using statistics actually have no proper mathematical training in it (like me, for example ).

 

Btw.: you'll soon realize that in mathematics it is very common to define the letters/objects being used, and not simply assume that everyone will correctly guess what sigma-x-one is (sry, could not resist this comment)

[noradetzky]

However poorly I've worded it this is simply an example of Propagation of Uncertainty. I guess I should review this as well because I'm obviously having trouble with the concept. The fact that these are uncorrelated means the final term for [math] (\frac{\sigma_f}{f})^2 [/math] is equal to zero because the vector uncertainties in combination with their respective vectors are orthogonal to all other vectors. The wiki on this is not the best either, try a year one physics book.

 

I don't have a first year physics book. But finding that Wiki subject was immensely helpful. Thanks!

 

 

Covariances for uncorrelated statistical variables vanish.

 

Oh. Right.

 

Btw.: you'll soon realize that in mathematics it is very common to define the letters/objects being used, and not simply assume that everyone will correctly guess what sigma-x-one is (sry, could not resist this comment)

 

What's this "definition" you speak of? Political sciences certainly don't need any, so why would physical sciences?

[The Observer]

What's this "definition" you speak of? Political sciences certainly don't need any, so why would physical sciences?

 

In all physical sciences it is absolutely essential to make very explicit the precise definitions for the technical and mathematical terms you are using since it often varies considerably from field to field.