The integrated nested Laplace approximation applied to spatial log-Gaussian Cox process models

References

• F.E. Bachl, F. Lindgren, D.L. Borchers, and J.B. Illian, inlabru: An R package for Bayesian spatial modelling from ecological survey data, Methods Ecol. Evol. 10 (2019), pp. 760–766.
   Web of Science ®Google Scholar
• A. Baddeley, J.F. Coeurjolly, E. Rubak, and R. Waagepetersen, Logistic regression for spatial Gibbs point processes, Biometrika 101 (2014), pp. 377–392.
   Web of Science ®Google Scholar
• A. Baddeley and R. Turner, Practical maximum pseudolikelihood for spatial point patterns, Aust. N. Z. J. Stat. 42 (2000), pp. 283–322.
   Web of Science ®Google Scholar
• A. Baddeley and R. Turner, Spatstat: An R package for analyzing spatial point patterns, J. Stat. Softw. 12 (2005), pp. 1–42.
   Web of Science ®Google Scholar
• A. Baddeley, R. Turner, J. Møller, and M. Hazelton, Residual analysis for spatial point processes, J. R. Stat. Soc. Ser. B (Stat. Methodol.) 67 (2005), pp. 617–666.
   Web of Science ®Google Scholar
• H. Bakka, H. Rue, G.A. Fuglstad, A. Riebler, D. Bolin, J. Illian, E. Krainski, D. Simpson, and F. Lindgren, Spatial modeling with r-inla: A review, Wiley Interdiscip. Rev. Comput. Stat. 10 (2018), p. e1443.
   Google Scholar
• H. Bakka, J. Vanhatalo, J.B. Illian, D. Simpson, and H. Rue, Non-stationary Gaussian models with physical barriers, Spat. Stat. 29 (2019), pp. 268–288.
   Web of Science ®Google Scholar
• M. Berman and T.R. Turner, Approximating point process likelihoods with GLIM, Appl. Stat. 41 (1992), pp. 31–38.
   Web of Science ®Google Scholar
• M. Blangiardo and M. Cameletti, Spatial and Spatio-temporal Bayesian Models with R-INLA, New York: Wiley, 2015.
   Google Scholar
• A. Brix and J. Møller, Space-time multi-type log Gaussian Cox processes with a view to modelling weeds, Scand. J. Stat. 28 (2001), pp. 471–488.
   Web of Science ®Google Scholar
• S. Buckland, E. Rexstad, T. Marques, and C. Oedekoven, Distance Sampling: Methods and Applications, New York: Springer, 2015.
   Google Scholar
• A. Chakraborty, A.E. Gelfand, A.M. Wilson, A.M. Latimer, and J.A. Silander, Point pattern modelling for degraded presence-only data over large regions, J. R. Stat. Soc. Ser. C (Appl. Stat.) 60 (2011), pp. 757–776.
   Web of Science ®Google Scholar
• D.R. Cox, Some statistical methods connected with series of events, J. R. Stat. Soc. Ser. B (Methodol.) 17 (1955), pp. 129–157.
   Google Scholar
• N. Cressie, Statistics for Spatial Data, New York: Wiley, 1993.
   Google Scholar
• P. Diggle, Statistical Analysis of Spatial and Spatio-temporal Point Patterns, 3rd ed., Boca Raton, FL: CRC Press, 2013.
   Google Scholar
• K.A. Flagg, A. Hoegh, and J.J. Borkowski, Modeling partially surveyed point process data: Inferring spatial point intensity of geomagnetic anomalies, J. Agric., Biol. Environ. Stat. 25 (2020) pp. 186–205.
   Web of Science ®Google Scholar
• G.A. Fuglstad, D. Simpson, F. Lindgren, and H. Rue, Constructing priors that penalize the complexity of Gaussian random fields, J. Am. Stat. Assoc. 114 (2019), pp. 445–452.
   Web of Science ®Google Scholar
• E. Gabriel, F. Bonneu, P. Monestiez, and J. Chadœuf, Adapted Kriging to predict the intensity of partially observed point process data, Spat. Stat. 18 (2016), pp. 54–71.
   Web of Science ®Google Scholar
• E. Gabriel, J. Coville, and J. Chadœuf, Estimating the intensity function of spatial point processes outside the observation window, Spat. Stat. 22 (2017), pp. 225–239.
   Web of Science ®Google Scholar
• J.B. Illian, S.H. Sørbye, and H. Rue, A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA), Ann. Appl. Stat. 6 (2012), pp. 1499–1530.
   Web of Science ®Google Scholar
• J.B. Illian, S.H. Sørbye, H. Rue, and D.K. Hendrichsen, Using inla to fit a complex point process model with temporally varying effects-a case study, J. Environ. Stat. 3 (2012), pp 1–21.
   Google Scholar
• M. Jullum, Investigating mesh-based approximation methods for the normalization constant in the log Gaussian Cox process likelihood, Stat 9 (2020), p. e285.
   Web of Science ®Google Scholar
• G. Konstantinoudis, D. Schuhmacher, H. Rue, and B.D. Spycher, Discrete versus continuous domain models for disease mapping, Spat. Spatiotemporal. Epidemiol. 32 (2020), p. 100319.
   Google Scholar
• E. Krainski, V. Gómez-Rubio, H. Bakka, A. Lenzi, D. Castro-Camilo, D. Simpson, F. Lindgren, and H. Rue, Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA, Boca Raton, FL: Chapman and Hall/CRC, 2018.
   Google Scholar
• Y. Li, P. Brown, D.C. Gesink, and H. Rue, Log Gaussian Cox processes and spatially aggregated disease incidence data, Stat. Methods Med. Res. 21 (2012), pp. 479–507.
   PubMed Web of Science ®Google Scholar
• F. Lindgren and H. Rue, Bayesian spatial modelling with R-INLA, J. Stat. Softw. 63 (2015), pp. 1–25.
   Web of Science ®Google Scholar
• F. Lindgren, H. Rue, and J. Lindström, An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach, J. R. Stat. Soc. Ser. B (Stat. Methodol.) 73 (2011), pp. 423–498.
   Web of Science ®Google Scholar
• W. Link and R. Barker, Bayesian Inference: With Ecological Applications, Boston: Elsevier, 2009.
   Google Scholar
• L. Lombardo, T. Opitz, and R. Huser, Point process-based modeling of multiple debris flow landslides using INLA: An application to the 2009 Messina disaster, Stoch. Environ. Res. Risk. Assess. 32 (2018), pp. 2179–2198.
   Web of Science ®Google Scholar
• D. MacKenzie, J. Nichols, J. Royle, K. Pollock, L. Bailey, and J. Hines, Occupancy Estimation and Modeling: Inferring Patterns and Dynamics of Species Occurrence, Boston: Elsevier, 2017.
   Google Scholar
• J. Møller, A.R. Syversveen, and R.P. Waagepetersen, Log Gaussian Cox processes, Scand. J. Stat. 25 (1998), pp. 451–482.
   Web of Science ®Google Scholar
• J. Møller and R.P. Waagepetersen, Statistical Inference and Simulation for Spatial Point Processes, Boca Raton, FL: CRC Press, 2003.
   Google Scholar
• J. Møller and R. Waagepetersen, Modern spatial point process modelling and inference, Scand. J. Stat. 34 (2007), pp. 643–711.
   Web of Science ®Google Scholar
• J. Neyman and E.L. Scott, Statistical approach to problems of cosmology, J. R. Stat. Soc. Ser. B (Methodol.) 20 (1958), pp. 1–43.
   Google Scholar
• S. Pereira, K.F. Turkman, L. Correia, and H. Rue, Unemployment estimation: Spatial point referenced methods and models, Spat. Stat. 41 (2019), p. 100345.
   Google Scholar
• H. Rue, S. Martino, and N. Chopin, Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations, J. R. Stat. Soc. Ser. B (Stat. Methodol.) 71 (2009), pp. 319–392.
   Web of Science ®Google Scholar
• H. Rue, A. Riebler, S.H. Sørbye, J.B. Illian, D.P. Simpson, and F.K. Lindgren, Bayesian computing with inla: A review, Annu. Rev. Stat. Appl. 4 (2017), pp. 395–421.
   Web of Science ®Google Scholar
• P. Samartsidis, C.R. Eickhoff, S.B. Eickhoff, T.D. Wager, L.F. Barrett, S. Atzil, T.D. Johnson, and T.E. Nichols, Bayesian log-Gaussian Cox process regression: Applications to meta-analysis of neuroimaging working memory studies, J. R. Stat. Soc. Ser. C (Appl. Stat.) 68 (2019), pp. 217–234.
   PubMed Web of Science ®Google Scholar
• L. Serra, M. Saez, J. Mateu, D. Varga, P. Juan, C. Díaz-Ávalos, and H. Rue, Spatio-temporal log-Gaussian Cox processes for modelling wildfire occurrence: The case of Catalonia, 1994–2008, Environ. Ecol. Stat. 21 (2014), pp. 531–563.
   Web of Science ®Google Scholar
• D. Simpson, J.B. Illian, F. Lindgren, S.H. Sørbye, and H. Rue, Going off grid: Computationally efficient inference for log-Gaussian Cox processes, Biometrika 103 (2016), pp. 49–70.
   Web of Science ®Google Scholar
• D. Simpson, F. Lindgren, and H. Rue, In order to make spatial statistics computationally feasible, we need to forget about the covariance function, Environmetrics 23 (2012), pp. 65–74.
   Web of Science ®Google Scholar
• D. Simpson, F. Lindgren, and H. Rue, Think continuous: Markovian Gaussian models in spatial statistics, Spat. Stat. 1 (2012), pp. 16–29.
   Web of Science ®Google Scholar
• D. Simpson, H. Rue, A. Riebler, T.G. Martins, and S.H. Sørbye, Penalising model component complexity: A principled, practical approach to constructing priors, Stat. Sci. 32 (2017), pp. 1–28.
   Web of Science ®Google Scholar
• S.H. Sørbye, J.B. Illian, D.P. Simpson, D. Burslem, and H. Rue, Careful prior specification avoids incautious inference for log-Gaussian Cox point processes, J. R. Stat. Soc. Ser. C (Appl. Stat.) 68 (2019), pp. 543–564.
   Web of Science ®Google Scholar
• M. Taddy, Autoregressive mixture models for dynamic spatial Poisson processes: Application to tracking intensity of violent crime, J. Am. Stat. Assoc. 105 (2010), pp. 1403–1417.
   Web of Science ®Google Scholar
• Y. Yuan, F.E. Bachl, F. Lindgren, D.L. Borchers, J.B. Illian, S.T. Buckland, H. Rue, and T. Gerrodette, Point process models for spatio-temporal distance sampling data from a large-scale survey of blue whales, Ann. Appl. Stat. 11 (2017), pp. 2270–2297.
   Web of Science ®Google Scholar