In this paper we introduce a new method for performing computational
inference on log-Gaussian Cox processes (LGCP). Contrary to current practice,
we do not approximate by a counting process on a partition of the domain, but
rather attack the point process likelihood directly. In order to do this, we
use the continuously specified Markovian random fields introduced by
\citet{Lindgren2011}. The inference is performed using the \texttt{R-INLA}
package of \citet{art451}, which allows us to perform fast approximate
inference on quite complicated models. The new method is tested on a real point
pattern data set as well as two interesting extensions to the classical LGCP
framework. The first extension considers the very real problem of variable
sampling effort throughout the observation window and implements the method of
\citet{Chakraborty2011}. The second extension moves beyond what is possible
with current techniques and constructs a log-Gaussian Cox process on the
world's oceans.

Code for the examples can be found at
https://sites.google.com/a/r-inla.org/www/examples/case-studies/simpson2011