The Exploratory Analysis of Bivariate Spatial Point Patterns Using Cross-Spectra

Mugglestone, M. A.; Renshaw, Eric

doi:10.1002/(sici)1099-095x(199607)7:4<361::aid-env217>3.0.co;2-u

Cited by 16 publications

(9 citation statements)

References 4 publications

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“…He applies a one-sided competition process. Mugglestone and Renshaw (1996) defined cross-spectral functions, called gain spectra, which can be used if a causal relationship between the components of a bivariate process is suspected.…”

Section: Introductionmentioning

confidence: 99%

Multitype Spatial Point Patterns with Hierarchical Interactions

HöUgmander¹,

SäUrkkä²

1999

Biometrics

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Multitype spatial point patterns with hierarchical interactions are considered. Here hierarchical interaction means directionality: points on a higher level of hierarchy affect the locations of points on the lower levels, but not vice versa. Such relations are common, for example, in ecological communities. Interacting point patterns are often modeled by Gibbs processes with pairwise interactions. However, these models are inherently symmetric, and the hierarchy can be acknowledged only when interpreting the results. We suggest the following in allowing the inclusion of the hierarchical structure in the model. Instead of regarding the pattern as a realization of a stationary multivariate point process, we build the pattern one type at a time according to the order of the hierarchy by using nonstationary univariate processes. As interactions connected to points x on a certain level are considered, the effect of the higher levels is interpreted as heterogeneity of the pattern x, and the points on the lower levels are neglected because of the hierarchical structure.

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Section: Introductionmentioning

confidence: 99%

Multitype Spatial Point Patterns with Hierarchical Interactions

HöUgmander¹,

SäUrkkä²

1999

Biometrics

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“…As

ζ_{i j} false({bolds, bolds}^{'} false) = ζ_{j i} false({bolds}^{'}, bolds false)

, we have ζ i j ( c ) = ζ ji ( − c ) and κ i j ( c )= κ ji ( − c ) under stationarity of

boldN = {false(N_{i}, N_{j} false)}^{sans-serifT}

(cf. Mugglestone & Renshaw, , ).…”

Section: Classical Analysis Of Qualitatively and Quantitatively Markementioning

confidence: 99%

“…This section discusses the auto‐ and cross‐spectral characteristics of marked point processes, which are based on Fourier transformations of (marked) point locations, as discussed by Bartlett (), Renshaw and Ford (, ), Mugglestone and Renshaw (, , ), and Renshaw (, ). The reader is also referred to Daley and Vere‐Jones () for the more technical details of this section.…”

Section: Spectral Characteristics Of Spatial Point Patternsmentioning

confidence: 99%

Partial characteristics for marked spatial point processes

Eckardt

Mateu

2019

Environmetrics

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This paper introduces a new class of partial summary characteristics for two types of marked planar point processes. We consider purely qualitatively marked spatial point processes and multitype spatial point processes with quantitative marks. After a survey of classical functional summary characteristics for qualitatively and quantitatively marked point processes, the class of partial characteristics is presented. These characteristics are defined through the periodogram, which makes the computations efficient. We demonstrate the application of our method in the analysis of a multispecies tree data recorded in the City of Melbourne.

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“…is the Fourier transform of the complete auto-covariance function of the point process (see Bartlett, 1964;Mugglestone and Renshaw, 1996) and f Y Y (!) is the Fourier transform of the auto-covariance function of the lattice process (see Priestley, 1996).…”

Section: Accepted M Manuscriptmentioning

confidence: 99%

“…This approach is analogous to the analysis carried out by Mugglestone and Renshaw (1996) to investigate properties of a bivariate spatial point process. Furthermore, it is an extension of the cross-spectral analysis used for one-dimensional hybrid processes: a one-dimensional hybrid process is a process with two components where one component is a one-dimensional point process and the other is a time series (see Rigas, 1983;Brillinger, 1994).…”

Section: Introductionmentioning

confidence: 99%