IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v60y2013icp146-156.html
   My bibliography  Save this article

Bayesian dynamic models for space–time point processes

Author

Listed:
  • Reis, Edna A.
  • Gamerman, Dani
  • Paez, Marina S.
  • Martins, Thiago G.

Abstract

In this work we propose a model for the intensity of a space–time point process, specified by a sequence of spatial surfaces that evolve dynamically in time. This specification allows flexible structures for the components of the model, in order to handle temporal and spatial variations both separately and jointly. These structures make use of state-space and Gaussian process tools. They are combined to create a richer class of models for the intensity process. This structural approach allows for a decomposition of the intensity into purely temporal, purely spatial and spatio-temporal terms. Inference is performed under a fully Bayesian approach, with the description of simulation-based and analytic methods for approximating the posterior distributions. The proposed methodology is applied to model the incidence of impulses in the small intestine, illustrated by a data-set obtained through an experiment conducted in cats, in order to understand the interaction between the nervous and digestive systems. This application illustrates the usefulness of the proposed methodology and shows it compares favorably against existing alternatives. The paper is concluded with a few directions for further investigation.

Suggested Citation

  • Reis, Edna A. & Gamerman, Dani & Paez, Marina S. & Martins, Thiago G., 2013. "Bayesian dynamic models for space–time point processes," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 146-156.
    • Handle: RePEc:eee:csdana:v:60:y:2013:i:c:p:146-156
    DOI: 10.1016/j.csda.2012.11.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312003994
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.11.008?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. Anders Brix & Peter J. Diggle, 2001. "Spatiotemporal prediction for log‐Gaussian Cox processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 823-841.
    2. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    3. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    5. Anders Brix & Jesper Moller, 2001. "Space‐time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 471-488, September.
    6. Liu, Hua & Brown, Donald E., 2003. "Criminal incident prediction using a point-pattern-based density model," International Journal of Forecasting, Elsevier, vol. 19(4), pages 603-622.
    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. Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2012. "Spatio-Temporal Model for a Random Set Given by a Union of Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 883-894, September.
    2. Mayer Alvo & Jingrui Mu, 2023. "COVID-19 Data Analysis Using Bayesian Models and Nonparametric Geostatistical Models," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    3. David Jiménez-Hernández & Víctor González-Calatayud & Ana Torres-Soto & Asunción Martínez Mayoral & Javier Morales, 2020. "Digital Competence of Future Secondary School Teachers: Differences According to Gender, Age, and Branch of Knowledge," Sustainability, MDPI, vol. 12(22), pages 1-16, November.
    4. Massimo Bilancia & Giacomo Demarinis, 2014. "Bayesian scanning of spatial disease rates with integrated nested Laplace approximation (INLA)," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 71-94, March.
    5. Douglas R. M. Azevedo & Marcos O. Prates & Dipankar Bandyopadhyay, 2021. "MSPOCK: Alleviating Spatial Confounding in Multivariate Disease Mapping Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 464-491, September.
    6. Braulio-Gonzalo, Marta & Bovea, María D. & Jorge-Ortiz, Andrea & Juan, Pablo, 2021. "Which is the best-fit response variable for modelling the energy consumption of households? An analysis based on survey data," Energy, Elsevier, vol. 231(C).
    7. Isabel Martínez-Pérez & Verónica González-Iglesias & Valentín Rodríguez Suárez & Ana Fernández-Somoano, 2021. "Spatial Distribution of Hospitalizations for Ischemic Heart Diseases in the Central Region of Asturias, Spain," IJERPH, MDPI, vol. 18(23), pages 1-10, November.
    8. Maike Tahden & Juliane Manitz & Klaus Baumgardt & Gerhard Fell & Thomas Kneib & Guido Hegasy, 2016. "Epidemiological and Ecological Characterization of the EHEC O104:H4 Outbreak in Hamburg, Germany, 2011," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-19, October.
    9. Zhang, Shen & Liu, Xin & Tang, Jinjun & Cheng, Shaowu & Qi, Yong & Wang, Yinhai, 2018. "Spatio-temporal modeling of destination choice behavior through the Bayesian hierarchical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 537-551.
    10. Shuangshuang Xu & Marco A. R. Ferreira & Erica M. Porter & Christopher T. Franck, 2023. "Bayesian model selection for generalized linear mixed models," Biometrics, The International Biometric Society, vol. 79(4), pages 3266-3278, December.
    11. Zhao, Qing & Boomer, G. Scott & Silverman, Emily & Fleming, Kathy, 2017. "Accounting for the temporal variation of spatial effect improves inference and projection of population dynamics models," Ecological Modelling, Elsevier, vol. 360(C), pages 252-259.
    12. Møller, Jesper & Torrisi, Giovanni Luca, 2007. "The pair correlation function of spatial Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 995-1003, June.
    13. Darren J. Mayne & Geoffrey G. Morgan & Bin B. Jalaludin & Adrian E. Bauman, 2018. "Does Walkability Contribute to Geographic Variation in Psychosocial Distress? A Spatial Analysis of 91,142 Members of the 45 and Up Study in Sydney, Australia," IJERPH, MDPI, vol. 15(2), pages 1-24, February.
    14. Luca Grassetti & Laura Rizzi, 2019. "The determinants of individual health care expenditures in the Italian region of Friuli Venezia Giulia: evidence from a hierarchical spatial model estimation," Empirical Economics, Springer, vol. 56(3), pages 987-1009, March.
    15. White, Staci A. & Herbei, Radu, 2015. "A Monte Carlo approach to quantifying model error in Bayesian parameter estimation," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 168-181.
    16. Ferreira, Marco A.R. & Porter, Erica M. & Franck, Christopher T., 2021. "Fast and scalable computations for Gaussian hierarchical models with intrinsic conditional autoregressive spatial random effects," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    17. John M. Humphreys, 2022. "Amplification in Time and Dilution in Space: Partitioning Spatiotemporal Processes to Assess the Role of Avian-Host Phylodiversity in Shaping Eastern Equine Encephalitis Virus Distribution," Geographies, MDPI, vol. 2(3), pages 1-16, July.
    18. Christopher Wikle & Mevin Hooten, 2010. "A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 417-451, November.
    19. Faustin Habyarimana & Temesgen Zewotir & Shaun Ramroop, 2017. "Structured Additive Quantile Regression for Assessing the Determinants of Childhood Anemia in Rwanda," IJERPH, MDPI, vol. 14(6), pages 1-15, June.
    20. Medina-Olivares, Victor & Calabrese, Raffaella & Dong, Yizhe & Shi, Baofeng, 2022. "Spatial dependence in microfinance credit default," International Journal of Forecasting, Elsevier, vol. 38(3), pages 1071-1085.

    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:eee:csdana:v:60:y:2013:i:c:p:146-156. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.