Quick inference for log Gaussian Cox processes with non-stationary underlying random fields

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F19%3A43899299" target="_blank" >RIV/60076658:12510/19:43899299 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/19:10401361

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S2211675319301393" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2211675319301393</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.spasta.2019.100388" target="_blank" >10.1016/j.spasta.2019.100388</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Quick inference for log Gaussian Cox processes with non-stationary underlying random fields

Popis výsledku v původním jazyce

For point patterns observed in natura, spatial heterogeneity is more the rule than the exception. In numerous applications, this can be mathematically handled by the flexible class of log Gaussian Cox processes (LGCPs); in brief, a LGCP is a Cox process driven by an underlying log Gaussian random field (log GRF). This allows the representation of point aggregation, point vacuum and intermediate situations, with more or less rapid transitions between these different states depending on the properties of GRF. Very often, the covariance function of the GRF is assumed to be stationary. In this article, we give two examples where the sizes (that is, the number of points) and the spatial extents of point clusters are allowed to vary in space. To tackle such features, we propose parametric and semiparametric models of non-stationary LGCPs where the non-stationarity is included in both the mean function and the covariance function of the GRF. Thus, in contrast to most other work on inhomogeneous LGCPs, second-order intensity-reweighted stationarity is not satisfied and the usual two step procedure for parameter estimation based on e.g. composite likelihood does not easily apply. Instead we propose a fast three step procedure based on composite likelihood. We apply our modelling and estimation framework

Název v anglickém jazyce

Quick inference for log Gaussian Cox processes with non-stationary underlying random fields

Popis výsledku anglicky

For point patterns observed in natura, spatial heterogeneity is more the rule than the exception. In numerous applications, this can be mathematically handled by the flexible class of log Gaussian Cox processes (LGCPs); in brief, a LGCP is a Cox process driven by an underlying log Gaussian random field (log GRF). This allows the representation of point aggregation, point vacuum and intermediate situations, with more or less rapid transitions between these different states depending on the properties of GRF. Very often, the covariance function of the GRF is assumed to be stationary. In this article, we give two examples where the sizes (that is, the number of points) and the spatial extents of point clusters are allowed to vary in space. To tackle such features, we propose parametric and semiparametric models of non-stationary LGCPs where the non-stationarity is included in both the mean function and the covariance function of the GRF. Thus, in contrast to most other work on inhomogeneous LGCPs, second-order intensity-reweighted stationarity is not satisfied and the usual two step procedure for parameter estimation based on e.g. composite likelihood does not easily apply. Instead we propose a fast three step procedure based on composite likelihood. We apply our modelling and estimation framework

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA19-04412S" target="_blank" >GA19-04412S: Nové přístupy k modelování a statistice náhodných množin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Spatial Statistics

ISSN

2211-6753

e-ISSN

—

Svazek periodika

2019

Číslo periodika v rámci svazku

33

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

23

Strana od-do

1-23

Kód UT WoS článku

000489753700003

EID výsledku v databázi Scopus

2-s2.0-85072734675