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Posterior Models

In: Bayesian Spatial Modelling with Conjugate Prior Models

Author

Listed:
  • Henning Omre

    (Norwegian University of Science and Technology, Department of Mathematical Sciences)

  • Torstein M. Fjeldstad

    (Norwegian Computing Center)

  • Ole Bernhard Forberg

    (Norwegian University of Science and Technology, Department of Mathematical Sciences)

Abstract

This chapter contains developments of the posterior models uniquely defined by the likelihood and prior models. These developments are performed for the Gaussian, Poisson and Markov models, which represent spatial continuous, event and mosaic variables, respectively. The pairs of likelihood and prior models are defined to be conjugate, and hence, the posterior models are analytically developed. Realisations of the spatial variables conditioned on the observations, based on the posterior model, can be generated. Algorithms for generating such realisations are specified. Furthermore, spatial predictions with quantified uncertainties are provided based on the posterior models. The posterior models for the hierarchical prior models are also developed. The running examples are continued.

Suggested Citation

  • Henning Omre & Torstein M. Fjeldstad & Ole Bernhard Forberg, 2024. "Posterior Models," Springer Books, in: Bayesian Spatial Modelling with Conjugate Prior Models, chapter 0, pages 85-114, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-65418-3_7
    DOI: 10.1007/978-3-031-65418-3_7
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