lines 8-58 of file: example/python/mixed/hes_random_obj_xam.py

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ran_likelihood: Example and Test
################################

p(u|theta)
**********
In this example there is not date and

.. math::

   - \log [ \B{p} ( u | \theta ]
   =
   \theta_0 u_0 u_1 + \theta_1 u_1 u_2 + \cdots + \theta_{m-1} u_{m-1} u_0

where :math:`m` is the number of fixed and random effects.


Derivative
**********
For this example there is no data.
Hence the partial of the random effects objective,
w.r.t the random effect :math:`u_i` is

.. math::

   \theta_i u_{i+1 \mod m} + \theta_{i-1 \mod m} u_{i-1 \mod m}


Hessian
*******
Taking the partial of the expression above
w.r.t the random effects :math:`u_{i-1 \mod m}` we obtain

.. math::

   \theta_{i-1 \mod m}

Taking the partial of the expression above
w.r.t the random effects :math:`u_{i+1 \mod m}` we obtain

.. math::



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