On Apr 14, 7:07 pm, Ray Koopman <koop...@sfu.ca> wrote:
On Apr 14, 12:08 pm,
mixit...@gmail.com wrote:
On Apr 14, 3:48 pm, Ray Koopman <koop...@sfu.ca> wrote:
On Apr 14, 9:36 am,
mixit...@gmail.com wrote:
Hi all,
I have a very trivial question for many of you, but for some reason my
mind wasn't getting around it to sit down and crack the question, so I
thought I'd post it on here.
I'm trying to fit simulated data to some experimental ones...and in
theory I know that the function should be: y = f(x^3).
so when I'm trying to get the best fit by minimizing the least squares
functions, should I look at minimizing the following function:
chi_square = sum of ((y_exp - y_sim)^2)
or should I be considering minimizing (the one that made more sense to
me):
chi_square = sum of ((y_exp^(1/3)-(y_sim^(1/3))^2
Thanks for your help in advance.
_F_
You should probably be doing something like the first rather than the
second. In either case, what you are calling "chi_square" probably
does not have a chi-square distribution. In general, how you should
fit depends on what you think the errors distributions are. Are they
the same for all values of x? Are you working with discrete values
(e.g., counts) or continuous measures? And what about the simulated
values? If these are based on some "number of simulations" then they
too will have errors. Or are you using the term in a broader sense, to
mean simply "theoretical"?
Well in my case I'm using a theoretical model and trying to find the
best fit parameter.
my function as I stated earlier has the form of y = A.x^3 (where A is
what I'm trying to find. A is actually an equation by itself but it
has one unknown parameter that I want to locate.)
The only reason I thought the second would be better, is because at
large x values, the error becomes more significant than at low x
values if I simply use the first expression. However, I would like to
keep the weight to be equal for all data points.
I am basically looking at the variation of Energy with Velocity, so
for every given velocity there will be a given experimentally measured
energy and another simulated one.
So at high velocities a 10% error would then weigh much more than a
10% error at small velocities and could then influence the fit.
Or should I use the sum of relative errors to be my criterion?
function to minimize = sum of [(y_exp-y_sim)/y_exp]^2
Unless you say something specific about how the error distributions
of the measured and simulated y relate to the corresponding true
values, you won't be able to give more than a hand-waving defense
of whatever fitting procedure you use. Working at that level, I'd
probably minimize sum{ [ log(y_exp) - log(y_sim) ]^2 }.
minimizing sum{ [ log(y_exp) - log(y_sim) ]^2 } actually makes the
most sense to me now and this is what I will be working on (since that
transformation will linearize the whole expression).
However, how "defendable" is to minimize the sum of residual errors
though (or the sum of squared residual errors)? Does something like
that have been used in the literature before?
