On Thu, Aug 30, 2007 at 12:52:33AM -0700, Andrew Lentvorski wrote: > Todd Walton wrote: > > >5 : statistically independent ... An oversimplification. > > Wikipedia has a nice discussion about the various uses of "orthogonal". > http://en.wikipedia.org/wiki/Orthogonality > > I tend to use it in the sense of "a and b are two characteristics, > variables, methods, etc. which comprise a larger space of many > variables, methods, etc. If a change in a causes no change in b, they > are orthogonal." > > I will also use the word "independent". ... When discussing probability and statistics, the word "orthogonal" is likely to mean "uncorrelated". "Independent" has a different and much stronger meaning. Roughly speaking, a and b are independent if knowing one does not give _any_ information about the other. a and b are uncorrelated (orthogonal) if the best _linear_ function (best in the sense of least mean square error) to predict one from the other is a constant.
It happens that if a and b are (jointly) Gaussian, i.e. normally distributed, then they are independent if and only if they are uncorrelated. On the other hand, if a is Gaussian with mean 0 and b=|a| or b=a*a, a and b are uncorrelated but b can be exactly predicted knowing a. b is totally dependent. Stewart Strait -- [email protected] http://www.kernel-panic.org/cgi-bin/mailman/listinfo/kplug-list
