The stochastic reconstruction approach for point processes aims at producing independent patterns with the same properties as the observed pattern, without specifying any particular model. Instead a so-called energy functional is defined, based on a set of point process summary characteristics. It measures the dissimilarity between the observed pattern (input) and another pattern. The reconstructed pattern (output) is sought iteratively by minimising the energy functional. Hence, the output has approximately the same values of the prescribed summary characteristics as the input pattern. In this paper, we focus on inhomogeneous point patterns and apply formal hypotheses tests to check the quality of reconstructions in terms of the intensity function and morphological properties of the underlying point patterns. We argue that the current version of the algorithm available in the literature for inhomogeneous point processes does not produce outputs with appropriate intensity function. We propose modifications to the algorithm which can remedy this issue.
Stochastic reconstruction Point process Summary characteristics Inhomogeneous process Intensity function
Mathematics Subject Classification (2010)
This is a preview of subscription content, log in to check access.
Baddeley A, Møller J, Waagepetersen RP (2000) Non-and semiparametric estimation of interaction in inhomogeneous point patterns. Stat Neerl 54:329–350CrossRefzbMATHGoogle Scholar
Baddeley A, Rubak E, Turner R (2015) Spatial Point patterns: Methodology and Applications with R. Chapman & hall/CRC, Boca RatonCrossRefzbMATHGoogle Scholar
Daley D, Vere-Jones D (2008) An Introduction to the Theory of Point Processes. Volume II: General Theory and Structure, 2nd edn. Springer, New YorkCrossRefzbMATHGoogle Scholar
Getzin S, Wiegand T, Hubbell SP (2014) Stochastically driven adult-recruit associations of tree species on Barro Colorado Island. Proc R Soc B 281:20140922CrossRefGoogle Scholar
Illian J, Penttinen A, Stoyan H, Stoyan D (2004) Statistical Analysis and Modelling of Spatial Point Patterns. Wiley, ChichesterzbMATHGoogle Scholar
Jacquemyn H, Brys R, Honnay O, Roldán-Ruiz I, Lievens B, Wiegand T (2012) Nonrandom spatial structuring of orchids in a hybrid zone of three Orchis species. New Phytol 193:454–464CrossRefGoogle Scholar
Konasová K (2018) Stochastic reconstruction of random point patterns, Master thesis, Charles University, Czech Republic. Available online: http://hdl.handle.net/20.500.11956/98703 [cited 13. 12. 2018]
Lilleleht A, Sims A, Pommerening A (2014) Spatial forest structure reconstruction as a strategy for mitigating edge-bias in circular monitoring plots. For Ecol Manag 316:47–53CrossRefGoogle Scholar
Loosmore BN, Ford DE (2006) Statistical inference using the g or K point pattern spatial statistics. Ecology 87:1925–1931CrossRefGoogle Scholar
Møller J, Waagepetersen RP (2004) Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, Boca RatonzbMATHGoogle Scholar
Mrkvicka T, Hahn U, Myllymäki M (2018) A one-way ANOVA test for functional data with graphical interpretation. Available on arXiv:1612.03608 [cited 26. 11. 2018]
Mundo I, Wiegand T, Kanagaraj R, Kitzberger T (2013) Environmental drivers and spatial dependency in wildfire ignition patterns of northwestern Patagonia. J Environ Manag 123:77–87CrossRefGoogle Scholar