---------------------------------------------------
lines 7-229 of file: example/csv/predict_descend.py
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{xrst_begin csv.predict_descend}
{xrst_spell
    eps
    dage
    dtime
    const
    eps
    std
    Sincidence
}

Example Predicting From Self and a Descendant
#############################################

iota_true
*********
There are only two non-zero rate in this model, omega and the
parent value for *iota* (the model for incidence).
{xrst_code py}'''
omega_true = 0.01
iota_true  = 0.01
'''{xrst_code}

node_dict
*********
Keys are nodes and values are corresponding parent node:
{xrst_code py}'''
node_dict = {
    'n0' : ''   ,
    'n1' : 'n0' ,
    'n2' : 'n0' ,
}
'''{xrst_code}


age_grid, time_grid
*******************
The only rate for this example is *iota* and it is constant in
age and time so we use a very simple age and time grid:
{xrst_code py}'''
age_grid   = [0.0, 100.0]
time_grid  = [1980.0, 2020.0]
'''{xrst_code}

number_sample
*************
This is the number of samples of the posterior distribution
to generate for each successful fit. Note that each sample includes
values for all the dismod_at model variables-name . For this example
there is only one model variable *iota* .
{xrst_code py}'''
number_sample = 4000
'''{xrst_code}

descendant_std_factor
=====================
This is the
:ref:`csv.predict@Input Files@option_predict.csv@descendant_std_factor` .
This example checks that this factor is (is not) used when
predicting for the node that was fit
(for a descendant of the node that was fit).
{xrst_code py}'''
descendant_std_factor = 2.0
'''{xrst_code}




random_seed
***********
We us the current time in seconds to seed the random number generator:
{xrst_code py}'''
import time
random_seed = int( time.time() )
'''{xrst_code}

n_data, std_data
****************
There are *n_data* simulated measurements.
These measurements are a Gaussian with mean *iota_true*
and standard deviation *std_data* :
{xrst_code py}'''
n_data = 1
std_data = iota_true * 0.2
'''{xrst_code}

input_file
**********
Input CSV files that are placed in the fit directory:
{xrst_code py}'''
input_file = dict()
'''{xrst_code}

predict_integrand.csv
=====================
All the measurements and predictions
for this example are for Sincidence; i.e..
a direct measurement of iota:
{xrst_code py}'''
input_file['predict_integrand.csv']  = 'integrand_name\n'
input_file['predict_integrand.csv'] += 'Sincidence\n'
'''{xrst_code}
There are measurements for n0, but not for n1 or n2.
Thus node n0 will predict for itself and for n2
( n1 is not in :ref:`csv.predict_descend@input_file@fit_goal.csv` . )

option_fit.csv
==============
{xrst_code py}'''
input_file['option_fit.csv']  =  \
"""name,value
refit_split,false
"""
input_file['option_fit.csv'] += f'number_sample,{number_sample}\n'
input_file['option_fit.csv'] += f'random_seed,{random_seed}\n'
'''{xrst_code}

option_predict.csv
==================
{xrst_code py}'''
input_file['option_predict.csv']  =  'name,value\n'
input_file['option_predict.csv']  +=  \
    f'descendant_std_factor,{descendant_std_factor}\n'
'''{xrst_code}

fit_goal.csv
============
There will be no fit or predictions for n1:
{xrst_code py}'''
input_file['fit_goal.csv']  = 'node_name\n'
input_file['fit_goal.csv'] += 'n2'
'''{xrst_code}

node.csv
========
{xrst_code py}'''
input_file['node.csv'] = \
'node_name,parent_name\n'
for node_name in node_dict :
    parent_name = node_dict[node_name]
    input_file['node.csv'] += f'{node_name},{parent_name}\n'
'''{xrst_code}

covariate.csv
=============
{xrst_code py}'''
input_file['covariate.csv'] = 'node_name,sex,age,time,omega\n'
for node_name in [ 'n0', 'n1', 'n2' ] :
    for sex in [ 'female', 'male' ] :
        for age in age_grid :
            for time in time_grid :
                row   = f'{node_name},{sex},{age},{time},{omega_true}\n'
                input_file['covariate.csv'] += row
'''{xrst_code}

prior.csv
=========
uniform_eps_0.1 is uniform on the interval [eps,.1] where eps = 1e-6,
the mean, which is only used for initialization, is 0.03.
{xrst_code py}'''
input_file['prior.csv'] = \
"""name,density,mean,std,eta,lower,upper
uniform_eps_0.1,uniform,0.01,,,1e-6,0.1
"""
'''{xrst_code}

parent_rate.csv
===============
The parent rate for *iota* is has a uniform_eps_0.1 prior
and is constant w.r.t. age and time:
{xrst_code py}'''
input_file['parent_rate.csv'] = \
"""rate_name,age,time,value_prior,dage_prior,dtime_prior,const_value
iota,0.0,0.0,uniform_eps_0.1,,,
"""
'''{xrst_code}

child_rate.csv
==============
All the child rates (rate random effects) are zero
{xrst_code py}'''
input_file['child_rate.csv'] = 'rate_name,value_prior\n'
'''{xrst_code}

mulcov.csv
==========
There are no covariate multipliers
{xrst_code py}'''
input_file['mulcov.csv'] = 'covariate,type,effected,value_prior,const_value\n'
r'''{xrst_code}

Hessian of Likelihood
*********************
For this example, *iota* is the only model variable
(that does not have equal lower and upper bounds).
Let :math:`m` be *n_data* ,
:math:`sigma` be *std_data*, and
:math:`y_i` be the measurement values.
The negative log likelihood for the n0 fit is:

.. math::

    L( \iota , y ) = \frac{1}{2} \sum_{i=0}^{m}
        \log \left( 2 \pi \sigma^2 \right)
        +
        \left( \frac{y_i - \iota }{\sigma} \right)^2

The Hessian with respect to iota ( :math:`\iota` ) is

.. math::

    \frac{ \partial^2 }{\partial \iota^2} L = \frac{m}{ \sigma^2 }


Rest of Source Code
*******************
Below is the source code, except for the settings above.
{xrst_literal
    # BEGIN REST_OF_SOURCE
    # END REST_OF_SOURCE
}

{xrst_end csv.predict_descend}