Re: [boost] different matrix library?

Subject: Re: [boost] different matrix library?
From: Edward Grace (ej.grace_at_[hidden])
Date: 2009-08-18 16:12:17

On 18 Aug 2009, at 20:46, joel wrote:

> Edward Grace wrote:
>> No, it's more subtle than that.  Almost all of the time there will be
>> a difference between A and B, however this difference is just 'noise'
>> around zero. In order for there to be a meaningful difference the
>> natural random variations of the differences should be significantly
>> different from zero.
> What's the difference between this and "most of the time A and B go at
> the same speed" ?
> apologize my stats ignorance :)

No problem.

You are (I think) confusing probability and probability density.

If - for the sake of argument and to keep the maths easy - you assume  
that A and B are both continuous and normally distributed then so  
will their difference. [In practice neither of these assumptions are  
true but it doesn't change the basic point.]

This normal distribution of the differences will be normal too.  This  
distribution is a probability density - to obtain a probability you  
must integrate it over a region (dT).

   http://en.wikipedia.org/wiki/Probability_density_function

If that region has zero width then the probability will also be  
zero.  Therefore, the probability that you observe A and B going at  
the same speed (A-B == 0) is zero.

In other words, paraphrasing your comment,

  "All of the time you will observe A and B do not go at the same  
speed." [*]

That difference however can be an illusion (purely the result of  
chance).

-ed

[*] Due to the assumptions above being incorrect this may not be true  
- the discrete nature of the distribution can lead to differences  
that are exactly zero.

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