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2.4 Statistics for residual minimization

Function File: info = residmin_stat (f, p, settings)

Frontend for computation of statistics for a residual-based minimization.

settings is a structure whose fields can be set by optimset. With settings the computation of certain statistics is requested by setting the fields ret_<name_of_statistic> to true. The respective statistics will be returned in a structure as fields with name <name_of_statistic>. Depending on the requested statistic and on the additional information provided in settings, f and p may be empty. Otherwise, f is the model function of an optimization (the interface of f is described e.g. in nonlin_residmin, please see there), and p is a real column vector with parameters resulting from the same optimization.

Currently, the following statistics (or general information) can be requested (the ret_ is prepended so that the option name is complete):

ret_dfdp: Jacobian of model function with respect to parameters.

ret_covd: Covariance matrix of data (typically guessed by applying a factor to the covariance matrix of the residuals).

ret_covp: Covariance matrix of final parameters.

ret_corp: Correlation matrix of final parameters.

See also: curvefit_stat.

Further settings

The fields of the settings structure can be set with (octave)optimset.

For settings common to all frontends see Common frontend options.

Additional settings:

objf_type

Type of objective function of the optimization; must be specified in many cases. This determines which backends to use. Currently, there are only backends for the type "wls" (weighted least squares).

residuals

covd

Optional information on the result of optimization, residuals and covariance matrix of data, respectively.

weights

Array of weights applied to the residuals in the previous optimization. Dimensions must match those of the residuals.

dfdp

Can be set in the same way and has the same default as in nonlin_residmin ( see nonlin_residmin), but alternatively may already contain the computed Jacobian of the model function at the final parameters in matrix- or structure-form.

complex_step_derivative_f

Estimate Jacobian of model function with complex step derivative approximation. Use only if you know that your model function is suitable for this. No user function for the Jacobian (dfdp) must be specified.

Structure based parameter handling

Please see Parameter structures.

Backend information

Please see Residual optimization and choose backend from menu under ‘Statistics backends’.

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