Posterior Models

Henning Omre, Torstein M. Fjeldstad and Ole Bernhard Forberg
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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

Chapter Chapter 7 in Bayesian Spatial Modelling with Conjugate Prior Models, 2024, pp 85-114 from Springer

Abstract: 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.

Date: 2024
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DOI: 10.1007/978-3-031-65418-3_7

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