  In geostatistics, the design for data collection is central for accurate
prediction and parameter inference. One important class of geostatistical
models is log-Gaussian Cox process (LGCP) which is used extensively, for
example, in ecology. However, there are no formal analyses on optimal designs
for LGCP models. In this work, we develop a novel model-based experimental
design for LGCP modeling of spatiotemporal point process data. We propose a new
spatially balanced rejection sampling design which directs sampling to
spatiotemporal locations that are a priori expected to provide most
information. We compare the rejection sampling design to traditional balanced
and uniform random designs using the average predictive variance loss function
and the Kullback-Leibler divergence between prior and posterior for the LGCP
intensity function. Our results show that the rejection sampling method
outperforms the corresponding balanced and uniform random sampling designs for
LGCP whereas the latter work better for models with Gaussian models. We perform
a case study applying our new sampling design to plan a survey for species
distribution modeling on larval areas of two commercially important fish stocks
on Finnish coastal areas. The case study results show that rejection sampling
designs give considerable benefit compared to traditional designs. Results show
also that best performing designs may vary considerably between target species.
