How to fit the log Gaussian Cox process model

If I understand your question correctly, the functions lgcp.estK() and
lgcp.estpcf() in the "spatstat" package should help you to fit the model.
(These functions use the method of minimum contrast.)

I don't know about "predicting" the underlying random field.  This is
random, with a constant mean "mu" (so the estimated value of mu
is the ``point prediction'' of the field).  The functions mentioned above
provide estimates of mu (and of the variance sigma^2 of the random
field).

If you are interested in estimating the particular realisation of the random
field which gave rise to the observed point pattern, then it seems to me
that simply smoothing the observed pattern with density.ppp() is about as
good as anything that you might do.

     cheers,

         Rolf Turner

Hi,
   As far as I know, there exist some programs via the function INLA,
but I'm so curious if there is a specific function directly used to fit the
log Gaussian Cox process model and
predict the latent Gaussian field. That is, if I have a data points, then I
input it in the function and
don't need to revise the program. Thanks for your help.