title: Variational Expectation of Poisson
body: <p>I was wondering where the analytical form of the variational Expectation
  \int q(f)logp(y|f) df for the Poisson Likelihood comes from (when using a log link).</p>
  
  <p>In the documentation it is only mentioned that one can approximate the intractable likelihood,
  however I'm not familiar enough with the topic to know what exactly is used.</p>
  
  <pre><code>    let g(.) be the inverse-link function, then this likelihood represents
  
      p(y_i | f_i) = Poisson(y_i | g(f_i) * binsize)
  
      Note:binsize
      For use in a Log Gaussian Cox process (doubly stochastic model) where the
      rate function of an inhomogeneous Poisson process is given by a GP.  The
      intractable likelihood can be approximated by gridding the space (into bins
      of size 'binsize') and using this Poisson likelihood.
  </code></pre>
  
  <p>Could you maybe point me to that approximation method?</p>
  
  <p>Thanks.</p>