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lines 6-149 of file: example/max_fit_option.py
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{xrst_begin_parent max_fit_option}
{xrst_spell
  dage
  dtime
}

Example Using max_fit Option
############################
For this example everything is constant in age and 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 {n3, n4, n5, n6},
and the leaf nodes are {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 only non-zero dismod_at rate for this example is
:ref:`glossary@iota`.

Covariate
*********
There are no covariates for this example.

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,
this is the true value for *rate*
in node *n* at age *a*, time *t*, and covariate values *c*.
The values *a*, *t*. *c*, are not used by this function for this example.
{xrst_literal
   # BEGIN rate_true
   # END rate_true
}

y_i
===
The only simulated integrand for this example is :ref:`glossary@Sincidence`
which is a direct measurement of iota.
This data is simulated without any noise; i.e.,
the i-th measurement is simulated as
*y_i = rate_true('iota', None, None, n_i, None)* where *n_i* is the node.
The data is modeled as having noise even though there is no simulated 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.

max_fit_option
**************
This is the value of the :ref:`option_all_table@max_fit` option.
It is also the number of data values per leaf.
Thus the leaf nodes fit all their data while the other nodes only fit
a randomly chosen subset of their data.
{xrst_literal
   # BEGIN max_fit_option
   # END max_fit_option
}

perturb_optimization_scale
**************************
This is the value of the
:ref:`option_all_table@perturb_optimization_scale` option.
It is only included as an example of using this option and is not
necessary.
{xrst_literal
   # BEGIN perturb_optimization_scale
   # END perturb_optimization_scale
}

Parent Rate Smoothing
*********************
This is the iota smoothing used for the fit_node.
There are no :ref:`glossary@dage` or :ref:`glossary@dtime`
priors because there is only one age and one time point.

Value Prior
===========
The following is the value prior used for the root_node
{xrst_literal
   # BEGIN parent_value_prior
   # END parent_value_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 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 max_fit_option}