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lines 5-78 of file: example/user/binomial.py
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# {xrst_begin user_binomial.py}
# {xrst_comment_ch #}
#
# Fitting Binomial Data Example
# #############################
#
# Iota
# ****
# There is only one grid point in the parent and child smoothing
# for iota, hence they are constant with respect to age and time.
#
# Parent
# ======
# The value *iota_true*
# is the simulated true rate for *iota*
# for both the parent and two child nodes.
# 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
# =====
# The *iota*
# :ref:`model_variables@Random Effects, u@Child Rate Effects`
# are simulated with value zero.
# They are fit using
# a Gaussian prior with a mean zero and standard deviation 0.1.
#
# Other Rates
# ***********
# The :ref:`rate_table@parent_smooth_id` and
# :ref:`rate_table@child_smooth_id` are null for the other rates; i.e.,\
# the other rates are zero.
#
# Data
# ****
#
# Integrand
# =========
# All of the data is for the prevalence integrand.
# Since *iota* is constant, and the other rates are zero,
# the true prevalence is :math:`1 - \exp( - iota * age )` .
#
# meas_value
# ==========
# The prevalence data is simulate using a
# binomial distribution divided by its sample size.
# The mean of the binomial distribution
# is the sample size times the true prevalence.
#
# Sample Size
# ===========
# The sample size for each data point is chosen as follows:
# {xrst_literal
#  # BEGIN_SAMPLE_SIZE
#  # END_SAMPLE_SIZE
# }
#
# Density
# =======
# If the count, corresponding to the measured value, is greater than or equal
# a threshold, a Gaussian approximation is used, otherwise the
# :ref:`density_table@density_name@binomial` density is used.
# Note that the approximation seems to work well even when the
# threshold is zero.
#
# Source Code
# ***********
# {xrst_literal
#     BEGIN PYTHON
#     END PYTHON
# }
#
# {xrst_end user_binomial.py}