log Poisson probability mass of <code>y</code> given the log-rate <code>alpha + x * beta</code>,
where an intercept <code>alpha</code> is used that is allowed to vary with the
different observations. Dependent variable value <code>y</code> is used for all observations.
The number of rows of <code>x</code> must match the size of <code>alpha</code> and
the number of columns of <code>x</code> needs to match the size of the coefficient vector <code>beta</code>.
If <code>x</code> and <code>y</code> are data (not