[SciPy-User] confidence interval for leastsq fit

[Gael Varoquaux]

On Thu, Apr 28, 2011 at 06:18:45AM -0400, josef.pktd at gmail.com wrote:
> given the question is about optimize.leastsq, I assume this applies :

> http://en.wikipedia.org/wiki/Non-linear_least_squares#Parameter_errors.2C_confidence_limits.2C_residuals_etc.

> non-linear model with additive error  y = f(x, params) + err
> function f is differentiable.
> minimize quadratic loss
> parameter is in the interior of the parameter space if there are bounds

> all regression results of the linear model apply based on local
> (derivatives), asymptotic (normality) distribution using the Jacobian
> instead of the design matrix.

Correct but a few caveats:

    - These are asymptotic results: you need a lot of data
    - The Jacobian should be non singular
    - One should be sure that that there is only one minimum, or that the
      optimizer always falls in the same minimum

G