Index: Simpson 2016 - Going Off Grid LGCP Inference

Simpson 2016 - Going Off Grid LGCP Inference

Routing Summary

Full capture of Simpson, Illian, Lindgren, Sorbye and Rue (2016), Going off grid: Computationally efficient inference for log-Gaussian Cox processes (Biometrika; arXiv:1111.0641), plus a concept note on Gaussian random fields and kriging (in the cluster folder Spatial Fields Concept Notes).

• Need the paper on one page, motivating PyMC examples E07/E86/E79/E89, section map? → Simpson 2016 - Going Off Grid - Overview
• Need Poisson-process / LGCP likelihood and why lattices are wasteful? → Simpson 2016 - LGCP Likelihood and the Lattice Approximation
• Need the pseudo-Poisson off-grid likelihood (eq. 3-4)? → Simpson 2016 - Off-Grid Poisson-Form Likelihood
• Need Matern/SPDE/GMRF, Neumann boundary? → Simpson 2016 - Matern SPDE and GMRF Representation
• Need convergence rates (Thm 1-2, Cor. A1-A2)? → Simpson 2016 - Convergence Theory
• Need BCI trees, sampling effort, ocean examples? → Simpson 2016 - Examples BCI Sampling Effort and Ocean
• Need kriging / GRF / field-level inference background? → Spatial Fields - Gaussian Random Fields, Kriging and Field-Level Inference

Concept Map

Concept	Note	Type	Depends On	Key Result
IPP and LGCP likelihood; lattice approximation	Simpson 2016 - LGCP Likelihood and the Lattice Approximation	definition	none	binning is the dominant lattice error
Off-grid Poisson-form likelihood	Simpson 2016 - Off-Grid Poisson-Form Likelihood	theorem	LGCP	exact point term + quadrature integral
Matern SPDE, FEM weights	Simpson 2016 - Matern SPDE and GMRF Representation	definition	off-grid	$({\kappa }^{2}C+G-B)z\sim N(0,C)$
Convergence	Simpson 2016 - Convergence Theory	theorem	both	lattice $O(p^{-1})$ vs $O(p^{-2})$
Case studies	Simpson 2016 - Examples BCI Sampling Effort and Ocean	example	all	37 s to 24 s with coarsened mesh
GRF, kriging, field-level inference	Spatial Fields - Gaussian Random Fields, Kriging and Field-Level Inference	concept	SPDE	kriging mean/variance; spectral diagonalisation

Notes

• Simpson 2016 - Going Off Grid - Overview — CONTAINS: question, contributions, motivating examples, Source Map.
• Simpson 2016 - LGCP Likelihood and the Lattice Approximation — CONTAINS: IPP likelihood, LGCP, lattice GLMM, four criticisms, gridded PyMC HSGP sketch.
• Simpson 2016 - Off-Grid Poisson-Form Likelihood — CONTAINS: eq. 2-4, quadrature, dual mesh, numerical check code.
• Simpson 2016 - Matern SPDE and GMRF Representation — CONTAINS: Matern, SPDE, FEM matrices, boundary, meshing.
• Simpson 2016 - Convergence Theory — CONTAINS: Thm 1-2, A3-A5, Cor. A1-A2, Remark A2.
• Simpson 2016 - Examples BCI Sampling Effort and Ocean — CONTAINS: Sec. 7 case studies, Sec. 8 discussion.
• Spatial Fields - Gaussian Random Fields, Kriging and Field-Level Inference — CONTAINS: concept note, no raw source.

Sources

Simpson 2016 - Going Off Grid LGCP Inference (arXiv:1111.0641v3). LGCP original: Moller, Syversveen & Waagepetersen (1998, Scand. J. Stat.); no legal free copy was retrievable, covered here via Simpson et al.

See Also

Hilbert Space Gaussian Processes | Gaussian Process Regression | Spatial Models - BYM