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lines 5-85 of file: example/user/fit_sim.py
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# {xrst_begin user_fit_sim.py}
# {xrst_spell
#     exp
# }
# {xrst_comment_ch #}
#
# Fitting Simulated Data Example
# ##############################
#
# Parent Iota
# ***********
# The value *iota_parent_true*
# is the simulated true rate for *iota*
# for the parent.
# A uniform prior is used for the parent rate with
# *iota_parent_true* /100 as a lower limit,
# and ``1`` as the upper limit.
#
# Child Iota
# **********
# The *iota*
# :ref:`model_variables@Random Effects, u@Child Rate Effects`
# have a Gaussian prior with a mean zero and standard deviation 0.5.
# Note that ``exp(0.5)`` is approximately 1.6 so the confidence interval
# corresponding to +/- two standard deviations is approximately
# [ 1.0 / 3.2 , 3.2 ].
# There is only one grid point in the parent and child smoothing
# for iota, hence it is constant in age and time.
# In addition, the sum of the child rate effects is constrained to
# be zero.
#
# 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.
#
# Covariate Multiplier
# ********************
# There is one covariate multiplier on income and it affects the
# value of the rate *iota* for a particular data point.
# The income covariate has been normalized so it ranges between
# zero and one.
# The prior for this multiplier is an uniform on the interval
# [-2, +2].
# The true value for this multiplier, used to simulate data, is
# called *mulcov_income_iota_true* .
# Note that there is only one grid point in the covariate multiplier,
# hence it is constant in age and time.
#
# Data
# ****
# All of the data is for the prevalence integrand and has a standard
# deviation of 1e-3.
#
# Starting Point and Scaling
# **************************
# The variable values used to simulate truth are also used as a
# starting point and scaling point for optimizing the simulated data.
# The optimal point is expected to be different due to the measurement
# noise and noise in the simulated priors.
# Start at the truth gives us the best chance that optimizing
# the simulated data will not end up at some other location minimum.
#
# Simulated Priors
# ****************
# The :ref:`prior_sim_table-name` contains simulated values for the priors
# on the variables. This example checks that, for each simulation,
# the sum of the random effects is zero (because the zero sum option
# is chosen for *iota* ).
#
# Source Code
# ***********
# {xrst_literal
#     BEGIN PYTHON
#     END PYTHON
# }
#
# {xrst_end user_fit_sim.py}