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lines 5-95 of file: example/user/predict_fit.py
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# {xrst_begin user_predict_fit.py}
# {xrst_comment_ch #}
#
# Predict Average Integrand Using Results of a Fit
# ################################################
#
# Purpose
# *******
# This examples used the :ref:`fit both<fit_command@variables@both>` command
# to estimate the model variables.
# It then uses the :ref:`predict fit_var<predict_command@source@fit_var>`
# command to compute the
# :ref:`avg_integrand@Integrand, I_i(a,t)@susceptible`
# population :math:`S(a)` at age :math:`a = 50`.
#
# Note Table
# **********
# ::
#
#               north_america
#                /          \
#        united_states   canada
#
# Problem Parameters
# ******************
# The following values are used to simulate the data and set the priors
# for fitting the data:
# {xrst_literal
#       begin problem parameters
#       end problem parameters
# }
#
# Age and Time Values
# *******************
# The age and time values do not affect the fitting for this problem
# because all the functions are constant in age and time.
# This follows from the fact that all of the smoothings have one age
# and one time point.
#
# Rate Table
# **********
# The :ref:`rate_table-name` only specifies that the only
# :ref:`var_table@var_type@rate` variables are
# *iota* for the parent and children.
# In addition, it specifies the smoothings for these rates
# each of which has one grid point.
#
# Variables
# *********
# There are three model variables in this example:
#
# .. list-table::
#       :widths: auto
#
#       * - *iota_north_america*
#         - The true value for
#            :ref:`iota(a,t)<diff_eq@Incidence, iota(a, t)>` in north_america.
#       * - *canada_effect*
#         - The true model value for the canada
#            :ref:`child rate effect<model_variables@Random Effects, u@Child Rate Effects>` on iota.
#       * - *united_states_effect*
#         - The true model value for the united_states
#            :ref:`child rate effect<model_variables@Random Effects, u@Child Rate Effects>` on iota.
#
# Integrand Table
# ***************
# The :ref:`integrand_table-name` for this example includes
# :ref:`avg_integrand@Integrand, I_i(a,t)@Sincidence` and
# :ref:`avg_integrand@Integrand, I_i(a,t)@susceptible` .
#
# Data Table
# **********
# There are three measurements of *Sincidence*
# in the :ref:`data_table-name` , one for each node.
# No noise is added to the measurements, and the priors on
# *iota* are uniform, so the fit should correspond to the
# model values used to simulate the data.
#
# Avgint Table
# ************
# There are three predictions of the susceptible population at
# age 50 specified in the :ref:`avgint_table-name` , one for each node.
#
# Source Code
# ***********
# {xrst_literal
#       BEGIN PYTHON
#       END PYTHON
# }
#
# {xrst_end user_predict_fit.py}