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gaussfit - Least Squares and Robust Estimation
gaussfit is a least squares and robust estimator of an arbitrary
parameterized model to observed data. This program is a slight NEMO adapation
of the University of Texas program gaussfit.
This version of gaussfit
can be run in two modes. In the first mode an existing model and environment
file are given, which contain all the initial conditions to run the program.
In this mode the program runs exactly as in the original gaussfit program.
In the second mode the environment file is either created or modified
from the remaining environment variables based program keywords (in NEMO
style). This is triggered by using any (but the correct combination) of
those remaining parameters This approach will not work in all gaussfit
application, but are fine for small problems with a simple set of parameters.
This manual page merely serves as a reminder for the somewhat more efficient
NEMO mode to run large amounts of fits, but it is highly recommended to
read the GaussFit User Guide (see below).
The datafiles in gaussfit must
be specially formatted (MIDAS-like) table format. Two useful tools that
come with the gaussfit distribution are mkgf(1gaussfit)
mkgf will add a gaussfit header interactively to files that have data
in columnar format. cjoin will strip off leading lines, and extract columns
from different datafiles and put them into a single file. See also tabs(1NEMO)
for converting ascii tables to MIDAS format within NEMO.
parameters are recognized in any order if the keyword is also given:
Here is a sample model file for the linear least
squares problem: (y=a+bx, with no errors in x):
- The input model filename, which contains the mathematical description of
the model (see EXAMPLE below) to be used to fit the data, in a C-like programming
language. Within NEMO the model files can also be located anywhere in the
GAUSSPATH (unix) environment variable. No default.
- The input
environment filename. Initial parameters and relevant datafiles are described
in this file, wich is a list of FITS-header formatted keyword=value pairs.
This environment file can either be created from scratch (see remaining
paramters below), or an existing one is used. If left blank, a name with
an extension of model_file is replaced with ’env’.
of the datafile(s) in MIDAS format. Up to 99 datafiles can be used. See tabs(1NEMO)
how to format file this way. No default.
- Pairs of parameter
names and values, separated by a comma. If this keyword is used to update
an environment file, you only need to specify the pairs that will be different,
if it’s the first time around, you need to supply initial values for all
of the parameters in the model file. This parameter list translates into
a parameter file, fed to gaussfit, whose name is derived by replacing the
model_file extension with
- The asymptotic relative efficiency (ARE)
used by this Huber-type robust estimation method. Select only one value
for any of the following fair, huber, tukey, minsum keywords. Their value
should be in the range 0.8 - 0.95, the authors suggest 0.9 or 0.95. Note that
fair or huber ~ 0.8 approaches the minsum method. If none of these four were
selected, the standard least squares is used.
- see above.
- see above.
- Median type estimator, using Barrodale & Roberts algorithm.
Probably not good when more than one observation per equation of condition.
Set to 0 or 1. See also above.
- Use orthogonal regression M-estimate. It
measures the metric for goodness-of-fit orthogonally to the fitted function.
By default true, use this to turn it off. Although recommended if fair
or tukey is used, it *must* be used for huber.
To activate set to a non-zero value. Typically 0.0001.
factor by which lambda is decreased when a new chi-squared is less than
the old. To activate set to a non-zero value. Typically 0.1.
- Two methods
for iteration are provided. Newton’s method, and the method of iteratively
reweighted least squares (IRLS). Set this parameter to true if you want
to use IRLS since the default is Newton. Note: variances cannot be computed
in IRLS mode. See also double= below.
- Two styles of iteration are
provided. Single or double iteration.
- Maximum number of iterations
allowed. Default, if not used, will be 10.
- Relative tolerance.
- Set this to true if you want to attempt to use triangularize the matrix
of conditions (keeps the size of matrix down).
- Set this to true
if you want to see intermediate matrices.
- Set this to true if you
want to see the correlation matrix and standard deviations (sigma’s) of
the parameters. Files results_file.corr and results_file.cov will be created.
Co-variances of the parameters are listed in the parameter file.
- Output logfile for results. If not given, the name is derived from the model
by replacing it’s extension with log.
- Set this to turn on debugging
output to a file FTN, which contains a dump of the function interpreter.
By default it’s off.
- Scale paramter that gaussfit computes if a robust
estimation was employed. Exact meaning to be published. Placed at output
in the environment file.
- Variance of unit weight of the solution.
Placed at output in the environment file.
- If set, all input files
will be reset, and overwriting will be allowed. This applies to the parameter
and environment file. Only useful in case the program in run in NEMO mode.
- If set, at the end of the run, the parameter file
is read and the parameters and their errors (if available) are reported,
one at a line.
parameter a, b;
export(y - (a + b*x));
Input datafiles are in MIDAS format: columns separated by a TAB, the
first row containing the names of the columns, the second row their types,
and subsequent rows form the data.
The names of columns must correspond
to the observation and data variables in the model file, and variances
and co-variances can be given in a column x_x and x_y (or y_x) resp.
how to create a MIDAS table from an ascii table which contains 4 columns:
% tabs in=test.table out=test.tab col=x,y,x_x,y_y
The NEMO approach cannot easily handle cases where the parameters
Fixing parameters can only be done by editing the model file,
and either changing a parameter into a constant (this keeps the paramter
in the parameter file, or params= keyword), or adding constraints to the
model file. Examples are in the manual.
GaussFit: A System of Least
Squares and Robust Estimation, USERS MANUAL, by William H. Jeffreys, Micheal
J. Fitzpatrick., Barbara E. McArthur, and James E. McCartney. University of
Texas at Austin.
$NEMO/usr/tools/gaussfit/ V3.04 release
$NEMODAT/gaussfit repository of some example model files
ftp://clyde.as.utexas.edu/pub/gaussfit/ official (anonymous ftp) release
The following UNIX environment variables are used by gaussfit:
GAUSSFIT colon separated list of directories searched for model files
Barbara McArthur (email@example.com)
Source Code Copyright (C) 1987 by William H. Jefferys,
Michael J. Fitzpatrick and Barbara E. McArthur
All Rights Reserved.
Peter Teuben (this NEMO interface)
11-aug-92 first nemo version pjt
xx-apr-94 v3.04 new improved compiler, wobble fix, more env,... mca
14-Jul-94 (nemo) added second mode option to run gaussfit pjt
26-may-96 installed the 3.53 version (sep 95) pjt
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