Nonlinear Fitting: Extreme uncertainties on a very good fit

4 次查看（过去 30 天）
Niles Martinsen
Niles Martinsen 2012-7-16
Hi
I have some data (x, y) (no uncertainties on either x or y), which very nicely follows an exponentially decaying function. I use "nlinfit" to fit my model to the data, and when I visually inspect the fit, there is a very good correspondence between obtained fit and data.
However the uncertainties on my parameters are huge (as in 1e7, whereas the average y-value is around 7-8), and I don't know why. Here is the command i use
opts = statset('MaxIter',600, 'Display','iter', 'TolFun', 1e-10);
[b, r, J, COVB, mse] = nlinfit(data(M:end-N, 1), data(M:end-N, 2), model, guess, opts);
Nothing out of the ordinary. Does anyone have a good idea of what might be wrong?
I wanted to upload my data and m-file for you to test, but apparently that functionality is not present.
Best, Niles.
  2 个评论
Star Strider
Star Strider 2012-7-16
I don't understand what you mean by the uncertainties on the parameters. The standard deviations on the parameters will be given as:
std_b = sqrt(diag(COVB))
and the 95% confidence interval on each as:
ci = [b-1.96*std_b b+1.96*std_b]
Are they large and do they include zero? Is ‘mse’ large also?
Niles Martinsen
Niles Martinsen 2012-7-18
They are large, and 0 is not included. mse is only on the order of e-5, so very small.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Star Strider
Star Strider 2012-7-18
编辑：Star Strider 2012-7-18
The only reason I can think of for the large parameter variances (and all parameter estimates significantly different from zero) with a small MSE is that you have a large number of parameters relative to the size of the data set. If this is the problem, creating a second data set by interpolating the first to generate more points and then fitting it should result in approximately the same parameter estimates and MSE but with smaller variances.
You can upload your data set and code by pasting it to your original post (‘Edit’ at this point) or adding it as a comment. (If your data set is large, please provide a representative sample of it, including the start and end.)
EDIT: The other reason for large variances in the situation you describe, especially with parameters estimates significantly different from zero, is that the estimated parameter values themselves are large.

类别

在 Help Center 和 File Exchange 中查找有关 Box Plots 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by