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lines 5-87 of file: example/user/mulstd.py
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# {xrst_begin user_mulstd.py}
# {xrst_comment_ch #}
#
# Estimating Smoothing Standard Deviation Multiplies
# ##################################################
#
# Purpose
# *******
# This example uses a smoothing standard deviation multiplier
# :ref:`lambda<model_variables@Fixed Effects, theta@Smoothing Standard Deviation Multipliers, lambda>`
# to determine the standard deviation of the random effects.
#
# Problem Parameters
# ******************
# The following values are used to simulate and model the data:
# {xrst_literal
#     begin problem parameters
#     end problem parameters
# }
#
# Age and Time Values
# *******************
# The age and time values do not matter for this problem
# because all the functions are constant in age and time.
# This can be seen by the fact that all of the smoothing has one age
# and one time point.
#
# Variables
# *********
#
# Parent
# ======
# A constant value used to model
# :ref:`iota<avg_integrand@Rate Functions@iota_i(a,t)>`
# for the parent node.
#
# Children
# ========
# A fixed value is used for each of the
# :ref:`model_variables@Random Effects, u@Child Rate Effects`
# so that this example passes its test without having a lot of children.
# You could try increasing the number of children and simulating
# the rate random effect for each child.
#
# Data Table
# **********
# For this example, all the data is
# :ref:`avg_integrand@Integrand, I_i(a,t)@Sincidence`
# with a known standard deviation.
#
# Rate Table
# **********
# The :ref:`rate_table-name` only specifies that *iota* for the parent
# and children are non-zero.
#
# Prior Table
# ***********
#
# Parent
# ======
# The prior for the parent node *iota* is uniform with lower limit 1e-4,
# upper limit 1.0 and mean 0.1.
# Note that the mean is not really the mean of this uniform distribution
# and it is only used to get the initial starting and scaling point
# for the optimization; see :ref:`init_command-name` .
#
# Children
# ========
# The prior for the child nodes *iota* is Gaussian
# with mean zero and standard deviation one.
# This is so that the actual standard deviation is *lambda*  * 1
# which is equal to *lambda* .
#
# Fitting
# *******
# Source Code
# ***********
# {xrst_literal
#     BEGIN PYTHON
#     END PYTHON
# }
#
# {xrst_end user_mulstd.py}