Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation

Abstract

In this article, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not expressible in closed form but it is easy to simulate realizations under the model. We therefore explain how to use approximate Bayesian computation (ABC) to carry out statistical inference for this model. We suggest a method for model validation based on posterior predictions and global envelopes. We illustrate the ABC procedure and model validation approach using both simulated point patterns and a real data example.

Preferential Sampling for Bivariate Spatial Data

“…However, in order to supply a shared process specification under geostatistical modeling, employing GPs is most convenient. In this regard, recent work (Virhs et al, 2021) introduces spatial aggregation to a Gibbs process using a GP and offers the possibility of further PS investigation. Another path for future work involves spatio-temporal response data collection, opening the potential of spatial bias varying over time in the data collection.…”

Aspects of Statistical Analysis of Spatial Point Patterns

“…In this section, I consider three classes of parametric spatial point process models as examples: log-Gaussian Cox processes (LGCP) , Strauss processes (Strauss, 1975, Kelly and, and LGCP-Strauss processes (Vihrs et al, 2022). I briefly define these in the following subsections and refer to the above references for more details about these models.…”

“…There is a tendency for overestimating σ 2 unless the true value is above circa 3 in which case it is usually underestimated. Vihrs et al (2022) also found it to be difficult to make inference about the parameters of the Gaussian random field in an LGCP-Strauss process and related it to the fact that it can be difficult to see the effect of changes in the Gaussian random field from a realization of the process because it is obscured by the small scale regularity.…”

“…The plots indicate that the point pattern exhibit repulsive behaviour at a small scale and some clustering at a larger scale. As an example, I now show how the neural network approach can be used to fit an LGCP-Strauss process to this point pattern (an LGCP-Strauss process model was previously fitted to this data in Vihrs et al (2022)).…”

“…Then, the above methods are not feasible. An example of such a point process model is the LGCP-Strauss process presented in Vihrs et al (2022) where the authors found it necessary to consider parameter estimation in a Bayesian setup because it was then possible to use the method of approximate Bayesian computations (ABC) which is based entirely on the ability to simulate under the model (see e.g. the overview of some ABC methods in ).…”