Changeset a7c6f38 in sasview for src/sas/sasgui/perspectives/fitting/media

Timestamp:

Mar 4, 2018 6:07:55 PM (7 years ago)

Author:

butler

Branches:

master, magnetic_scatt, release-4.2.2, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, unittest-saveload

Children:

84ac3f1

Parents:

943e17a

Message:

Clarify use of chi^{2 in GUI and documentation}

Changed Gui name and tooltip to reflect we are using reduced chi^{2 not
simply Chi}2/Npts. Also edited the documenataion to finish making that
clear and in the process cleaned up a few old (i.e. incorrect)
statements.

Location:

src/sas/sasgui/perspectives/fitting/media

Files:

• fitting_help.rst (modified) (3 diffs)
• residuals_help.rst (modified) (2 diffs)

src/sas/sasgui/perspectives/fitting/media/fitting_help.rst

@@ -426 +426 @@
 See :ref:`Assessing_Fit_Quality`.
 
-The objective of model-fitting is to find a *physically-plausible* model, and set
-of model parameters, that generate a theory that reproduces the experimental data
-and gives residual values as close to zero as possible.
+The objective of model-fitting is to find a *physically-plausible* model, and
+set of model parameters, that generate a theory that reproduces the experimental
+data and minimizes the values of the residuals.
 
 Change the default values of the model parameters by hand until the theory line
-starts to represent the experimental data. Then uncheck the tick boxes alongside
-all parameters *except* the 'background' and the 'scale'. Click the *Fit* button.
-SasView will optimise the values of the 'background' and 'scale' and also display
-the corresponding uncertainties on the optimised values.
-
-*NB: If no uncertainty is shown it generally means that the model is not very*
-*dependent on the corresponding parameter (or that one or more parameters are*
-*'correlated').*
-
-In the bottom left corner of the *Fit Page* is a box displaying the normalised value
-of the statistical $\chi^2$ parameter returned by the optimiser.
+starts to represent the experimental data. Then check the tick boxes alongside
+the 'background' and the 'scale' parameters. Click the *Fit* button. SasView
+will optimise the values of the 'background' and 'scale' and also display the
+corresponding uncertainties on the optimised values.
+
+.. note::
+   If a parameter uncertainty is unrealistically large, or if it displays as
+   NaN either the model is a poor representation of the data, the parameter in
+   question is either highly correlated with one or more other fitted parameters
+   or at least that the model is relatively insensitive to the value of that
+   particular parameter.
+
+In the bottom left corner of the *Fit Page* is a box displaying the normalised
+value of the statistical $\chi^2$ parameter returned by the optimiser.
 
 Now check the box for another model parameter and click *Fit* again. Repeat this
 process until most or all parameters are checked and have been optimised. As the
-fit of the theory to the experimental data improves the value of 'chi2/Npts' will
-decrease. A good model fit should easily produce values of 'chi2/Npts' that are
+fit of the theory to the experimental data improves, the value of 'Reduced Chi2'
+will decrease. A good model fit should produce values of Reduced Chi2 close
 close to one, and certainly <100. See :ref:`Assessing_Fit_Quality`.
 
@@ -512 +515 @@
 *FitPage*'s.
 
-Note that the chi2/Npts value returned is the SUM of the chi2/Npts of each fit. To
-see the chi2/Npts value for a specific *FitPage*, click the *Compute* button at the
-bottom of that *FitPage* to recalculate. Also see :ref:`Assessing_Fit_Quality`.
+Note that the Reduced Chi2 value returned is the SUM of the Reduced Chi2 of
+each fit. To see the Reduced Chi2 value for a specific *FitPage*, click the 
+*Compute* button at the bottom of that *FitPage* to recalculate. Note that in
+doing so the degrees of freedome will be set to Npts.
+See :ref:`Assessing_Fit_Quality`.
 
 Simultaneous Fits with Constraints
@@ -538 +543 @@
 *FitPage*'s.
 
-Note that the chi2/Npts value returned is the SUM of the chi2/Npts of each fit. To
-see the chi2/Npts value for a specific *FitPage*, click the *Compute* button at the
-bottom of that *FitPage* to recalculate. Also see :ref:`Assessing_Fit_Quality`.
-
+Note that the Reduced Chi2 value returned is the SUM of the Reduced Chi2 of
+each fit. To see the Reduced Chi2 value for a specific *FitPage*, click the 
+*Compute* button at the bottom of that *FitPage* to recalculate. Note that in
+doing so the degrees of freedome will be set to Npts.
+See :ref:`Assessing_Fit_Quality`.  Moreover in the case of constraints the
+degrees of freedom are less than one might think do to those constraints.
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
 

src/sas/sasgui/perspectives/fitting/media/residuals_help.rst

@@ -27 +27 @@
 
 $\chi^2$ is a statistical parameter that quantifies the differences between
-an observed data set and an expected dataset (or 'theory').
-
-When showing the a model with the data, *SasView* displays this parameter
-normalized to the number of data points, $N_\mathrm{pts}$ such that
+an observed data set and an expected dataset (or 'theory') calculated as
 
 .. math::
 
-  \chi^2_N
-  =  \sum[(Y_i - \mathrm{theory}_i)^2 / \mathrm{error}_i^2] / N_\mathrm{pts}
+  \chi^2
+  =  \sum[(Y_i - \mathrm{theory}_i)^2 / \mathrm{error}_i^2]
 
-When performing a fit, *SasView* instead displays the reduced $\chi^2_R$,
-which takes into account the number of fitting parameters $N_\mathrm{par}$
-(to calculate the number of 'degrees of freedom'). This is computed as
+Fitting typically minimizes the value of $\chi^2$.  However, for assessing the
+quality of the model and its "fit" this parameter is not terribly helpful on its
+own.  Thus *SasView* instead displays a normalized version of this parameter,
+using the traditional reduced $\chi^2_R$.  This is the $\chi^2$ divided by the
+degrees of freedom (or DOF). The DOF is simply the number of data points being
+considered reduced by the number of free (i.e. fitted) parameters. Note that
+model parameters that are kept fixed do *not* contribute to the DOF (they are
+not"free". This reduced value is then given as
 
 .. math::
@@ -47 +49 @@
   / [N_\mathrm{pts} - N_\mathrm{par}]
 
-The normalized $\chi^2_N$ and the reduced $\chi^2_R$ are very close to each
-other when $N_\mathrm{pts} \gg N_\mathrm{par}$.
+where $N_\mathrm{par}$ is the number of *fitted* parameters. Note that this
+means the displayed value will vary depending on the number of parameters used
+in the fit.  In particular, when doing a calculation without a fit (e.g.
+manually changing a parameter) the DOF will now equal $N_\mathrm{pts}$ and the
+$\chi^2_R$ will be the smallest possible for that combination of model, data
+set and set of parameter values.
+
+When $N_\mathrm{pts} \gg N_\mathrm{par}$ as it should for proper fitting, the
+value of the reduced $\chi^2_R$ will not change very much.
 
 For a good fit, $\chi^2_R$ tends to 1.