×

Regularized estimation for highly multivariate log Gaussian Cox processes. (English) Zbl 1437.62274

Summary: Statistical inference for highly multivariate point pattern data is challenging due to complex models with large numbers of parameters. In this paper, we develop numerically stable and efficient parameter estimation and model selection algorithms for a class of multivariate log Gaussian Cox processes. The methodology is applied to a highly multivariate point pattern data set from tropical rain forest ecology.

MSC:

62J07 Ridge regression; shrinkage estimators (Lasso)
62M30 Inference from spatial processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
62P12 Applications of statistics to environmental and related topics

Software:

glmnet
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Baddeley, A.; Jammalamadaka, A.; Nair, G., Multitype point process analysis of spines on the dendrite network of a neuron, J. R. Stat. Soc. Ser. C (Appl. Stat.), 63, 5, 673-694 (2014) · doi:10.1111/rssc.12054
[2] Chilès, J-P; Delfiner, P., Geostatistics: Modeling Spatial Uncertainty. Probability and Statistics (1999), New York: Wiley, New York · Zbl 0922.62098
[3] Choi, J.; Oehlert, G.; Zou, H., A penalized maximum likelihood approach to sparse factor analysis, Stat. Interface, 3, 4, 429-436 (2010) · Zbl 1245.62074 · doi:10.4310/SII.2010.v3.n4.a1
[4] Choiruddin, A.; Coeurjolly, J-F; Letué, F., Convex and non-convex regularization methods for spatial point processes intensity estimation, Electron. J. Stat., 12, 1, 1210-1255 (2018) · Zbl 1473.62324 · doi:10.1214/18-EJS1408
[5] Coeurjolly, J-F; Møller, J.; Waagepetersen, R., A tutorial on Palm distributions for spatial point processes, Int. Stat. Rev., 85, 3, 404-420 (2017) · Zbl 07763562 · doi:10.1111/insr.12205
[6] Condit, R., Tropical Forest Census Plots (1998), Berlin, Germany and Georgetown, Texas: Springer-Verlag and R. G. Landes Company, Berlin, Germany and Georgetown, Texas
[7] Condit, R.; Hubbell, Sp; Foster, Rb, Changes in tree species abundance in a neotropical forest: impact of climate change, J. Trop. Ecol., 12, 2, 231-256 (1996) · doi:10.1017/S0266467400009433
[8] Diggle, P.; Zheng, P.; Durr, P., Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK, J. Roy. Stat. Soc. Ser. C (Appl. Stat.), 54, 3, 645-658 (2005) · Zbl 1490.62352 · doi:10.1111/j.1467-9876.2005.05373.x
[9] Friedman, J.; Hastie, T.; Tibshirani, R., Regularization paths for generalized linear models via coordinate descent, J. Stat. Softw., 33, 1, 1-22 (2010) · doi:10.18637/jss.v033.i01
[10] Guan, Y., A least-squares cross-validation bandwidth selection approach in pair correlation function estimations, Stat. Probab. Lett., 77, 18, 1722-1729 (2007) · Zbl 1129.62027 · doi:10.1016/j.spl.2007.04.016
[11] Hastie, Trevor; Friedman, Jerome; Tibshirani, Robert, Model Inference and Averaging, The Elements of Statistical Learning, 225-256 (2001), New York, NY: Springer New York, New York, NY · Zbl 0973.62007
[12] Hastie, T.; Tibshirani, R.; Wainwright, M., Statistical Learning with Sparsity: The Lasso and Generalizations (2015), Boca Raton: Chapman & Hall/CRC Press, Boca Raton · Zbl 1319.68003
[13] Hoerl, A.E., Kennard, R.W.: Ridge regression. Encyclopedia Stat. Sci. 8 (1988) · Zbl 0536.62054
[14] Hubbell, Sp; Foster, Rb; Sutton, Sl; Whitmore, Tc; Chadwick, Ac, Diversity of canopy trees in a neotropical forest and implications for conservation, Tropical Rain Forest: Ecology and Management, 25-41 (1983), Oxford: Blackwell Scientific Publications, Oxford
[15] Jalilian, A.; Waagepetersen, R., Fast bandwidth selection for estimation of the pair correlation function, J. Stat. Comput. Simul., 88, 10, 2001-2011 (2018) · Zbl 07192643 · doi:10.1080/00949655.2018.1428606
[16] Jalilian, A.; Guan, Y.; Mateu, J.; Waagepetersen, R., Multivariate product-shot-noise Cox models, Biometrics, 71, 4, 1022-1033 (2015) · Zbl 1400.62266 · doi:10.1111/biom.12339
[17] Lan, G.; Getzin, S.; Wiegand, T.; Hu, Y.; Xie, G.; Zhu, H.; Cao, M., Spatial distribution and interspecific associations of tree species in a tropical seasonal rain forest of China, PLoS ONE, 7, 9, e46074 (2012) · doi:10.1371/journal.pone.0046074
[18] Lee, Jd; Sun, Y.; Saunders, Ma, Proximal Newton-type methods for minimizing composite functions, SIAM J. Optim., 24, 3, 1420-1443 (2014) · Zbl 1306.65213 · doi:10.1137/130921428
[19] Møller, J.; Waagepetersen, R., Statistical Inference and Simulation for Spatial Point Processes (2003), Boca Raton: Chapman and Hall/CRC, Boca Raton
[20] Møller, J.; Waagepetersen, R., Modern statistics for spatial point processes, Scand. J. Stat., 34, 4, 643-684 (2007) · Zbl 1157.62067
[21] Møller, J.; Syversveen, Ar; Waagepetersen, R., Log Gaussian Cox processes, Scand. J. Stat., 25, 3, 451-482 (1998) · Zbl 0931.60038 · doi:10.1111/1467-9469.00115
[22] Rajala, T.; Murrell, Dj; Olhede, Sc, Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection, J. R. Stat. Soc.: Ser. C (Appl. Stat.), 67, 5, 1237-1273 (2018) · doi:10.1111/rssc.12281
[23] Simon, N.; Friedman, J.; Hastie, T.; Tibshirani, R., A sparse-group lasso, J. Comput. Graph. Stat., 22, 2, 231-245 (2013) · doi:10.1080/10618600.2012.681250
[24] Thurman, Al; Fu, R.; Guan, Y.; Zhu, J., Regularized estimating equations for model selection of clustered spatial point processes, Statistica Sinica, 25, 1, 173-188 (2015) · Zbl 1400.62117
[25] Tibshirani, R., Regression shrinkage and selection via the lasso, J. R. Stat. Soc. Ser. B (Stat. Methodol.), 58, 1, 267-288 (1996) · Zbl 0850.62538
[26] Tibshirani, R.; Saunders, M.; Rosset, S.; Zhu, J.; Knight, K., Sparsity and smoothness via the fused lasso, J. R. Stat. Soc. Ser. B (Stat. Methodol.), 67, 1, 91-108 (2005) · Zbl 1060.62049 · doi:10.1111/j.1467-9868.2005.00490.x
[27] Waagepetersen, R., An estimating function approach to inference for inhomogeneous Neyman-Scott processes, Biometrics, 63, 1, 252-258 (2007) · Zbl 1122.62073 · doi:10.1111/j.1541-0420.2006.00667.x
[28] Waagepetersen, R.; Guan, Y.; Jalilian, A.; Mateu, J., Analysis of multi-species point patterns using multivariate log Gaussian Cox processes, J. Roy. Stat. Soc. Ser. C (Appl. Stat.), 65, 1, 77-96 (2016) · doi:10.1111/rssc.12108
[29] Zou, H.; Hastie, T., Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B (Stat. Methodol.), 67, 2, 301-320 (2005) · Zbl 1069.62054 · doi:10.1111/j.1467-9868.2005.00503.x
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.