Log Gaussian Cox processes on the sphere

Publikation: Bog/antologi/afhandling/rapportRapportForskning

Resumé

We define and study the existence of log Gaussian Cox processes (LGCPs)
for the description of inhomogeneous and aggregated/clustered point patterns
on the d-dimensional sphere, with d = 2 of primary interest. Useful theoretical
properties of LGCPs are studied and applied for the description of sky
positions of galaxies, in comparison with previous analysis using a Thomas
process. We focus on simple estimation procedures and model checking based
on functional summary statistics and the global envelope test.
OriginalsprogEngelsk
ForlagCSGB, Institut for Matematik, Aarhus Universitet
Antal sider14
StatusUdgivet - 2018
NavnCSGB Research Report
Nummer4
Vol/bind2018

Fingerprint

Cox Process
Gaussian Process
Galaxies
Model Checking
Envelope
Statistics

Emneord

    Citer dette

    Pacheco, F. A. C., & Møller, J. (2018). Log Gaussian Cox processes on the sphere. CSGB, Institut for Matematik, Aarhus Universitet. CSGB Research Report, Nr. 4, Bind. 2018
    Pacheco, Francisco Andrés Cuevas ; Møller, Jesper. / Log Gaussian Cox processes on the sphere. CSGB, Institut for Matematik, Aarhus Universitet, 2018. 14 s. (CSGB Research Report; Nr. 4, Bind 2018).
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    abstract = "We define and study the existence of log Gaussian Cox processes (LGCPs)for the description of inhomogeneous and aggregated/clustered point patternson the d-dimensional sphere, with d = 2 of primary interest. Useful theoreticalproperties of LGCPs are studied and applied for the description of skypositions of galaxies, in comparison with previous analysis using a Thomasprocess. We focus on simple estimation procedures and model checking basedon functional summary statistics and the global envelope test.",
    keywords = "H{\"o}lder continuity, minimum contrast estimation, model checking, point processes on the sphere, reduced Palm distribution, second order intensity reweighted homogeneity",
    author = "Pacheco, {Francisco Andr{\'e}s Cuevas} and Jesper M{\o}ller",
    year = "2018",
    language = "English",
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    Pacheco, FAC & Møller, J 2018, Log Gaussian Cox processes on the sphere. CSGB Research Report, nr. 4, bind 2018, CSGB, Institut for Matematik, Aarhus Universitet.

    Log Gaussian Cox processes on the sphere. / Pacheco, Francisco Andrés Cuevas; Møller, Jesper.

    CSGB, Institut for Matematik, Aarhus Universitet, 2018. 14 s.

    Publikation: Bog/antologi/afhandling/rapportRapportForskning

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    AB - We define and study the existence of log Gaussian Cox processes (LGCPs)for the description of inhomogeneous and aggregated/clustered point patternson the d-dimensional sphere, with d = 2 of primary interest. Useful theoreticalproperties of LGCPs are studied and applied for the description of skypositions of galaxies, in comparison with previous analysis using a Thomasprocess. We focus on simple estimation procedures and model checking basedon functional summary statistics and the global envelope test.

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    KW - model checking

    KW - point processes on the sphere

    KW - reduced Palm distribution

    KW - second order intensity reweighted homogeneity

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    Pacheco FAC, Møller J. Log Gaussian Cox processes on the sphere. CSGB, Institut for Matematik, Aarhus Universitet, 2018. 14 s. (CSGB Research Report; Nr. 4, Bind 2018).