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lines 5-87 of file: example/user/fit_meas_noise.py
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# {xrst_begin user_fit_meas_noise.py}
# {xrst_comment_ch #}
#
# Group Measurement Noise Covariate Multipliers, Gamma
# ####################################################
#
# Purpose
# *******
# This example demonstrates fitting
# :ref:`model_variables@Fixed Effects, theta@Group Covariate Multipliers`
# that effect the measurement noise.
#
# Random Effects
# **************
# There are no random effects in this example.
#
# Iota
# ****
# The value *iota_true*
# is the simulated true rate for iota.
# The prior for iota is uniform prior with lower limit
# *iota_true / 100* and upper limit one.
# The mean for the prior is *iota_true / 10*
# (this is only used as a starting point for the optimization).
# There is only one grid point (one :ref:`model_variable<model_variables-name>` )
# corresponding to *iota* , hence it is constant in age and time.
#
# Other Rates
# ***********
# For this example the other rates are all zero.
# This is specified by setting the
# :ref:`rate_table@parent_smooth_id` and
# :ref:`rate_table@child_smooth_id` to null
# for the other rates.
#
# Subgroup Table
# **************
# The data is divided into two groups.
# The first group is hospital data and the second group is survey data.
#
# Covariate Multiplier
# ********************
# There is one covariate multiplier on the covariate column ``one``
# and the rate ``iota`` .
# This is a measurement noise covariate multiplier
# :ref:`gamma<data_like@Measurement Noise Covariates@gamma_j (a, t)>`
# that only effects the survey data.
# The prior for this multiplier is a uniform on the interval from zero
# to 10 * *gamma_true* .
# The true value for this multiplier, used to simulate data, is
# called *gamma_true* .
# The mean for the prior is ``gamma_true``  / 10
# (this is only used as a starting point for the optimization).
# There is only one grid point
# (one model variable) corresponding to the covariate multiplier,
# hence it is constant in age and time.
#
# Data
# ****
# There are *n_data* measurements of Sincidence.
# The hospital data has standard deviation *meas_std* .
# The survey data has addition noise determine by the covariate effect.
#
# meas_noise_effect
# *****************
# see :ref:`option_table@meas_noise_effect` .
# The function ``gamma_true`` depends on this option,
# this in turn affects the priors. Hence the data base must
# be recreated for each choice of this option
#
# Scaling Gamma
# *************
# The function ``gamma_true()`` shows on the scaling of *gamma*
# depends on the value of *meas_noise_effect* .
#
# Source Code
# ***********
# {xrst_literal
#     BEGIN PYTHON
#     END PYTHON
# }
#
# {xrst_end user_fit_meas_noise.py}