Bayesian model based spatiotemporal survey designs and partially observed log Gaussian Cox process

Abstract

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.

Effects of ignoring survey design information for data reuse

“…2010, Pati et al. 2011, Liu and Vanhatalo 2020). We note that including a spatial random effect in the southern seamount simulation is not an effective replacement for covariates and that all the design covariates need to be included (Fig.…”

“…We are also aware that this simple advice may be hard to implement in certain situations; an example is when all covariates are not available for all surveys utilised in a particular reuse. In these situations, careful and skilful analyses must be undertaken, which will rest on assumptions that are necessary to describe both the sampling process and ecological processes (Diggle et al, 2010;Pati et al, 2011;Liu and Vanhatalo, 2020). We note that including a spatial random effect in the southern seamount simulation is not an effective replacement for covariates and that all the design covariates need to be included (Fig.…”

Species Distribution Modeling with Expert Elicitation and Bayesian Calibration

“…We sampled in total 92 sites (Figure 1) which were dispersed over the entire study area covering all main habitat types. The sampling was scheduled to the a priori estimated peak larval season (Liu and Vanhatalo, 2020) in June. From each sample, we counted early-stage larvae (size range of 3-17 mm) and recorded the effort; that is, the volume of water sampled, which equals the length of the transect multiplied by the size (area) of the opening of the Gulf ichthyoplankton sampler.…”

“…We followed Liu and Vanhatalo (2020) and Kallasvuo et al (2017) and modeled the distribution of pikeperch larvae with a log Gaussian Cox process (LGCP) with intensity function λ(s, x(s)) where s denotes a location inside the study area and x(s) is a vector of environmental covariates at that location. We modeled the log intensity with a linear function of the covariates and a spatial random effect:…”

Parameterising cloud base updraft velocity of marine stratocumuli

“…On the other hand, one should not focus too heavily on any single region because of the diminishing return from each additional nearby point. As the designs are model-based, the aforementioned aspects imply two competing requirements of a design: i) the design should cover the entire domain of interest, and ii) it should focus on sub-regions of interest where a higher accuracy is desired (see also Liu and Vanhatalo (2020)).…”