-----------------------------------------
lines 6-161 of file: example/remission.py
-----------------------------------------

{xrst_begin_parent remission}
{xrst_spell
  dage
  dtime
}

Example Estimation With Remission and No Incidence Data
#######################################################
For this example everything is constant in time so the
functions below do not depend on time.

Nodes
*****
The following is a diagram of the node tree for this example.
The :ref:`glossary@root_node` is n0,
the :ref:`glossary@fit_goal_set` is equal to the leaf set
{n3, n4, n5, n6}::

                     n0
             /-----/\-----\
          n1              n2
         /  \            /  \
      n3    n4        n5    n6

fit_goal_set
============
{xrst_literal
    # BEGIN fit_goal_set
    # END fit_goal_set
}

Rates
*****
The non-zero dismod_at rates for this example are
:ref:`glossary@iota`, :ref:`glossary@rho`, and :ref:`glossary@omega`.
For *rate* equal to iota, rho, and omega,
we use *rate(a, n)* to denote the value for *rate*
as a function of age *a* and node *n*.


Covariate
*********
There are not covariates for this example.

Random Effects
**************
For each node, there is a random effect on iota an rho that is constant
in age and time. Note that the total effect for a leaf is the sum
of its random effect plus its parents random effect.

s_n
===
We use *s_n* to denote the sum of the random effects for node *n*.
The code below sets this sum using the name sum_random:
{xrst_literal
    # BEGIN sum_random
    # END sum_random
}

Simulated Data
**************

Random Seed
===========
The random seed can be used to reproduce results.
If the original value of this setting is zero, the clock is used get
a random seed. The actual value or *random_seed* is always printed.
{xrst_literal
    # BEGIN random_seed
    # END random_seed
}

rate_true(rate, a, t, n, c)
===========================
For *rate* equal to iota, rho, omega,
this is the true value for *rate*
in node *n* at age *a*, time *t*, and covariate values *c*.
The time and covariate list are not used.
{xrst_literal
    # BEGIN rate_true
    # END rate_true
}

y_i
===
The simulated integrand for this example are
:ref:`glossary@Sincidence`, and :ref:`glossary@prevalence`.
The data is simulated without any noise
but it is modeled as having noise.

n_i
===
Data is only simulated for the leaf nodes; i.e.,
each *n_i* is in the set { n3, n4, n5, n6 }.
Since the data does not have any nose, the data residuals are a measure
of how good the fit is for the nodes in the fit_goal_set.

a_i
===
For each leaf node, data is generated on the following *age_grid*:
{xrst_literal
    # BEGIN age_grid
    # END age_grid
}

Omega Constraints
*****************
The :ref:`omega_constraint-name` routine is used
to set the value of omega in the parent and child nodes.

Parent Rate Smoothing
*********************

iota
====
This is the smoothing used in the fit_node model for iota.
Note that the value part of this smoothing is only used for the *root_node*.
This smoothing uses the *age_gird* and one time point.
There are no :ref:`glossary@dtime` priors because there is only one time point.

Parent Rate Priors
==================
The following is the value and dage priors used for the root_node
{xrst_literal
    # BEGIN parent_prior
    # END parent_prior
}
The mean and standard deviation are only used for the root_node.
The :ref:`create_shift_db-name`
routine replaces them for other nodes.

Child Rate Smoothing
********************
This is the smoothing used for the
random effect for each child of the fit_node.
There are no :ref:`glossary@dage` or dtime
priors because there is only one age and one time point in this smoothing.

Value Prior
===========
The following is the value prior used for the children of the fit_node:
{xrst_literal
    # BEGIN child_value_prior
    # END child_value_prior
}

Checking The Fit
****************
The results of the fit are checked by check_cascade_node
using the :ref:`check_cascade_node@avgint_table`
that was created by the root_node_db routine.
The node_id for each row is replaced by the node_id for the
fit being checked.
routine uses these tables to check that fit against the truth.

{xrst_end remission}