Cox Processes Associated with Spatial Copula Observed through Stratified Sampling
Cox processes, also called doubly stochastic Poisson processes, are used for describing phenomena for which overdispersion exists, as well as Poisson properties conditional on environmental effects. In this paper, we consider situations where spatial count data are not available for the whole study...
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| Format: | Article |
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MDPI AG
2021-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/5/524 |
| _version_ | 1797415502934441984 |
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| author | Walguen Oscar Jean Vaillant |
| author_facet | Walguen Oscar Jean Vaillant |
| author_sort | Walguen Oscar |
| collection | DOAJ |
| description | Cox processes, also called doubly stochastic Poisson processes, are used for describing phenomena for which overdispersion exists, as well as Poisson properties conditional on environmental effects. In this paper, we consider situations where spatial count data are not available for the whole study area but only for sampling units within identified strata. Moreover, we introduce a model of spatial dependency for environmental effects based on a Gaussian copula and gamma-distributed margins. The strength of dependency between spatial effects is related with the distance between stratum centers. Sampling properties are presented taking into account the spatial random field of covariates. Likelihood and Bayesian inference approaches are proposed to estimate the effect parameters and the covariate link function parameters. These techniques are illustrated using Black Leaf Streak Disease (BLSD) data collected in Martinique island. |
| first_indexed | 2024-03-09T05:48:32Z |
| format | Article |
| id | doaj.art-cfe4b60181e54507965837a6220096de |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:48:32Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cfe4b60181e54507965837a6220096de2023-12-03T12:19:11ZengMDPI AGMathematics2227-73902021-03-019552410.3390/math9050524Cox Processes Associated with Spatial Copula Observed through Stratified SamplingWalguen Oscar0Jean Vaillant1Department of Mathematics and Computer Sciences, Université des Antilles, 97157 Pointe-à-Pitre, FranceDepartment of Mathematics and Computer Sciences, Université des Antilles, 97157 Pointe-à-Pitre, FranceCox processes, also called doubly stochastic Poisson processes, are used for describing phenomena for which overdispersion exists, as well as Poisson properties conditional on environmental effects. In this paper, we consider situations where spatial count data are not available for the whole study area but only for sampling units within identified strata. Moreover, we introduce a model of spatial dependency for environmental effects based on a Gaussian copula and gamma-distributed margins. The strength of dependency between spatial effects is related with the distance between stratum centers. Sampling properties are presented taking into account the spatial random field of covariates. Likelihood and Bayesian inference approaches are proposed to estimate the effect parameters and the covariate link function parameters. These techniques are illustrated using Black Leaf Streak Disease (BLSD) data collected in Martinique island.https://www.mdpi.com/2227-7390/9/5/524point processCox processcounting measureoverdispersionstratified samplingspatial copula |
| spellingShingle | Walguen Oscar Jean Vaillant Cox Processes Associated with Spatial Copula Observed through Stratified Sampling Mathematics point process Cox process counting measure overdispersion stratified sampling spatial copula |
| title | Cox Processes Associated with Spatial Copula Observed through Stratified Sampling |
| title_full | Cox Processes Associated with Spatial Copula Observed through Stratified Sampling |
| title_fullStr | Cox Processes Associated with Spatial Copula Observed through Stratified Sampling |
| title_full_unstemmed | Cox Processes Associated with Spatial Copula Observed through Stratified Sampling |
| title_short | Cox Processes Associated with Spatial Copula Observed through Stratified Sampling |
| title_sort | cox processes associated with spatial copula observed through stratified sampling |
| topic | point process Cox process counting measure overdispersion stratified sampling spatial copula |
| url | https://www.mdpi.com/2227-7390/9/5/524 |
| work_keys_str_mv | AT walguenoscar coxprocessesassociatedwithspatialcopulaobservedthroughstratifiedsampling AT jeanvaillant coxprocessesassociatedwithspatialcopulaobservedthroughstratifiedsampling |