IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v104y2020i3d10.1007_s10182-020-00373-6.html
   My bibliography  Save this article

A non-homogeneous Poisson process geostatistical model with spatial deformation

Author

Listed:
  • Fidel Ernesto Castro Morales

    (Universidade Federal do Rio Grande do Norte)

  • Lorena Vicini

    (Universidade Federal de Santa Maria)

Abstract

In this paper, we propose a geostatistical model for the counting process using a non-homogeneous Poisson model. This work aims to model the intensity function as the sum of two components: spatial and temporal. The spatial component is modeled using a Gaussian process in which the covariance structure is assumed to be anisotropic. Anisotropy is incorporated by applying a spatial deformation approach. The temporal component is modeled in such a way that its behavior concerning time has the structure of a Goel process. The inferences for the proposed model are obtained from a Bayesian perspective. The parameter estimation is obtained using Markov Chain Monte Carlo methods. The proposed model is adjusted to a set of real data, referring to the rain precipitation in 29 monitoring stations, distributed in the states of Maranhão and Piauí, in the northeast region of Brazil, in 31 years, from 01/01/1980 to 12/31/2010. The objective is to estimate the frequency of rain that exceeded a certain threshold.

Suggested Citation

  • Fidel Ernesto Castro Morales & Lorena Vicini, 2020. "A non-homogeneous Poisson process geostatistical model with spatial deformation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 503-527, September.
  • Handle: RePEc:spr:alstar:v:104:y:2020:i:3:d:10.1007_s10182-020-00373-6
    DOI: 10.1007/s10182-020-00373-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-020-00373-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10182-020-00373-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alexandra M. Schmidt & Anthony O'Hagan, 2003. "Bayesian inference for non‐stationary spatial covariance structure via spatial deformations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 743-758, August.
    2. J. Law, 2009. "Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology by LAWSON, A. B," Biometrics, The International Biometric Society, vol. 65(2), pages 661-662, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fidel Ernesto Castro Morales & Dimitris N. Politis & Jacek Leskow & Marina Silva Paez, 2022. "Student’s-t process with spatial deformation for spatio-temporal data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1099-1126, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marcelo Cunha & Dani Gamerman & Montserrat Fuentes & Marina Paez, 2017. "A non-stationary spatial model for temperature interpolation applied to the state of Rio de Janeiro," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(5), pages 919-939, November.
    2. Ephraim M. Hanks, 2017. "Modeling Spatial Covariance Using the Limiting Distribution of Spatio-Temporal Random Walks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 497-507, April.
    3. Isabelle Grenier & Bruno Sansó & Jessica L. Matthews, 2024. "Multivariate nearest‐neighbors Gaussian processes with random covariance matrices," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.
    4. Andrew Gordon Wilson & David A. Knowles & Zoubin Ghahramani, 2011. "Gaussian Process Regression Networks," Papers 1110.4411, arXiv.org.
    5. Joaquim Henriques Vianna Neto & Alexandra M. Schmidt & Peter Guttorp, 2014. "Accounting for spatially varying directional effects in spatial covariance structures," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 103-122, January.
    6. Hsu, Chia-Yueh & Chang, Shu-Sen & Lee, Esther S.T. & Yip, Paul S.F., 2015. "“Geography of suicide in Hong Kong: Spatial patterning, and socioeconomic correlates and inequalities”," Social Science & Medicine, Elsevier, vol. 130(C), pages 190-203.
    7. Pei-Sheng Lin, 2014. "Generalized Scan Statistics for Disease Surveillance," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 791-808, September.
    8. Horváth, Lajos & Kokoszka, Piotr & Wang, Shixuan, 2020. "Testing normality of data on a multivariate grid," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    9. Michele Guindani & Alan E. Gelfand, 2006. "Smoothness Properties and Gradient Analysis Under Spatial Dirichlet Process Models," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 159-189, June.
    10. Lina Zgaga & Felix Agakov & Evropi Theodoratou & Susan M Farrington & Albert Tenesa & Malcolm G Dunlop & Paul McKeigue & Harry Campbell, 2013. "Model Selection Approach Suggests Causal Association between 25-Hydroxyvitamin D and Colorectal Cancer," PLOS ONE, Public Library of Science, vol. 8(5), pages 1-11, May.
    11. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    12. Kirsner, Daniel & Sansó, Bruno, 2020. "Multi-scale shotgun stochastic search for large spatial datasets," Computational Statistics & Data Analysis, Elsevier, vol. 146(C).
    13. Khalid Al-Ahmadi & Sabah Alahmadi & Ali Al-Zahrani, 2019. "Spatiotemporal Clustering of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) Incidence in Saudi Arabia, 2012–2019," IJERPH, MDPI, vol. 16(14), pages 1-14, July.
    14. Bao, Jie & Yang, Zhao & Zeng, Weili & Shi, Xiaomeng, 2021. "Exploring the spatial impacts of human activities on urban traffic crashes using multi-source big data," Journal of Transport Geography, Elsevier, vol. 94(C).
    15. Bissiri, Pier Giovanni & Cleanthous, Galatia & Emery, Xavier & Nipoti, Bernardo & Porcu, Emilio, 2022. "Nonparametric Bayesian modelling of longitudinally integrated covariance functions on spheres," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    16. Thierno Souleymane Barry & Oscar Ngesa & Nelson Owuor Onyango & Henry Mwambi, 2021. "Bayesian Spatial Modeling of Anemia among Children under 5 Years in Guinea," IJERPH, MDPI, vol. 18(12), pages 1-18, June.
    17. Enrique Gracia & Antonio López-Quílez & Miriam Marco & Silvia Lladosa & Marisol Lila, 2014. "Exploring Neighborhood Influences on Small-Area Variations in Intimate Partner Violence Risk: A Bayesian Random-Effects Modeling Approach," IJERPH, MDPI, vol. 11(1), pages 1-17, January.
    18. Raphaël Huser & Marc G. Genton, 2016. "Non-Stationary Dependence Structures for Spatial Extremes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 470-491, September.
    19. Idris A. Eckley & Guy P. Nason & Robert L. Treloar, 2010. "Locally stationary wavelet fields with application to the modelling and analysis of image texture," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(4), pages 595-616, August.
    20. Laura Gosoniu & Penelope Vounatsou, 2011. "Non-stationary partition modeling of geostatistical data for malaria risk mapping," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(1), pages 3-13.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:alstar:v:104:y:2020:i:3:d:10.1007_s10182-020-00373-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.