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lines 5-80 of file: example/user/data_density.py
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# {xrst_begin user_data_density.py}
# {xrst_comment_ch #}
#
# Fit With Outliers Using Data Density Command
# ############################################
#
# Purpose
# *******
# This example first fits using a Gaussian data density.
# It uses the first fit as a starting point for another fit
# with a Student's-t data density.
# The :ref:`data_density_command-name` is used to change the data density.
#
# Problem Parameters
# ******************
# The following values are used to simulate and model the data:
# {xrst_literal
#     begin problem parameters
#     end problem parameters
# }
#
# Age and Time Values
# *******************
# The age and time values do not matter for this problem
# because all the functions are constant in age and time.
# This can be seen by the fact that all of the smoothing has one age
# and one time point.
#
# Variables
# *********
# The constant value used to model
# :ref:`iota<avg_integrand@Rate Functions@iota_i(a,t)>`
# for the parent node is only one model variable in this example.
#
# Data Table
# **********
# For this example, all the data is
# :ref:`avg_integrand@Integrand, I_i(a,t)@Sincidence` .
# The good data is Gaussian with mean *iota_true*
# and standard deviation *meas_cv* * *iota_true* .
# The outlier data has mean 10* *iota_true*
# and standard deviation 2* *iota_true* .
#
# Rate Table
# **********
# The :ref:`rate_table-name` only specifies that *iota* for the parent
# is the only nonzero rate for this example.
# In addition, it specifies the smoothing for that rate which has only
# one grid point. Hence there is only one model variable corresponding to
# the rates.
#
# Prior Table
# ***********
# The prior for *iota* is uniform with lower limit 1e-4,
# upper limit 1.0 and mean 0.1.
# Note that the mean is not really the mean of this uniform distribution
# and it is only used to get the initial starting and scaling point
# for the optimization; see :ref:`init_command-name` .
#
# Fitting
# *******
# A first fit is done using a Gaussian density for the data.
# This is used to get a better starting point for the optimization.
# All the density values in the data table are changed to be Students-t
# and a second fit is done.
# The results of the second fit are check for accuracy of the estimate
# and for proper detection of the outliers.
#
# Source Code
# ***********
# {xrst_literal
#     BEGIN PYTHON
#     END PYTHON
# }
#
# {xrst_end user_data_density.py}