Practical Approximations for Spatial Point Process Models

K. A. Flagg

19 February 2020

\[ \log(\lambda(u)) = \mathbf{z}'(u) \boldsymbol{\beta} + \mathbf{e}(u) \]

Plot of a random surface and a mesh approximation.

  • SPDE approach (Lindgren, Rue, and Lindström 2011)
    • Approximates GP with CAR process
  • Off the grid approach (Simpson et al. 2016)
    • Approximates PP with Poisson counts at SPDE nodes

References

Lindgren, Finn, Håvard Rue, and Johan Lindström. 2011. “An Explicit Link Between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73 (4): 423–98.

Simpson, Daniel, Janine B Illian, Finn Lindgren, Sigrunn H Sørbye, and Havard Rue. 2016. “Going Off Grid: Computationally Efficient Inference for Log-Gaussian Cox Processes.” Biometrika 103 (1): 49–70.