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lines 6-45 of file: example/user/no_random.cpp
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{xrst_begin no_random.cpp}

No Random Effects: Example and Test
###################################

Model
*****

.. math::

   \B{p}( z_i | \theta ) \sim \B{N} ( \theta_i , 1 )

.. math::

   \B{p}( \theta_i ) \sim \B{N} ( 0 , 1 )

The corresponding fixed likelihood
:ref:`g(theta)<theory@Fixed Likelihood, g(theta)>`
is

.. math::

   g( \theta ) = \frac{1}{2} \sum_{i} \left[
      \log ( 2 \pi ) + \theta_i^2
      +
      \log ( 2 \pi ) + ( z_i - \theta_i )^2
   \right]

The optimal solution (with no constraints) is

.. math::

   \hat{\theta}_i = z_i / 2

{xrst_literal
   // BEGIN C++
   // END C++
}

{xrst_end no_random.cpp}