Computational benchmarking of the INLA-SPDE approach for spatial point processes: parameter recovery and spatial confounding

{Monte Carlo simulation is used to benchmark the computational and inferential performance of the Log-Gaussian Cox Process estimated via the INLA-SPDE framework, with particular focus on parameter recovery, spatial confounding, and spatial range identifiability on bounded domains.} The Log-Gaussian Cox Process (LGCP) is a foundational framework for modelling spatial point patterns, yet exact Bayesian inference scales cubically with the number of spatial discretisation nodes. The Integrated Nested Laplace Approximation coupled with the Stochastic Partial Differential Equation (INLA-SPDE) approach resolves this bottleneck by exploiting a sparse Gaussian Markov Random Field representation, achieving a substantial reduction in computational complexity relative to exact covariance-based methods. Nevertheless, the empirical reliability of parameter recovery within this approximation, particularly under spatial confounding between fixed-effect covariates and latent Matérn fields, has not been systematically benchmarked. This paper presents a 500-replicate Monte Carlo simulation study to evaluate the inferential performance of the LGCP-INLA-SPDE pipeline using a highly controlled synthetic spatial domain with documented terrain-distance covariates and known ground-truth parameters. Monte Carlo standard errors are reported alongside all coverage estimates. Results demonstrate that the marginal variance is recovered with near-nominal accuracy, achieving 89%–91% credible interval coverage across spatial architectures. Fixed-effect terrain covariates exhibit mild but systematic undercoverage (90%–93%), providing an empirical characterisation of spatial confounding under the Laplace approximation. The simulation further confirms that when the true spatial range represents a restricted fraction of the domain width, coverage collapses to 55.8%, while marginal variance estimates remain unaffected. Despite these identifiability limits, the Watanabe-Akaike Information Criterion successfully discriminates covariate-driven models from intercept-only null baselines in 91%–99% of replicates. Sensitivity analysis confirms that fixed-effect inferences are robust across four distinctly different Penalized Complexity prior specifications. These findings establish the first systematic empirical characterisation of LGCP-INLA-SPDE parameter recovery and spatial confounding, providing clear computational benchmarks for practitioners.