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Bayesian Inference for Non-Markovian Point Processes

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Advances and Challenges in Space-time Modelling of Natural Events

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 207))

Abstract

The Bayesian approach to statistical inference has in recent years become very popular, especially in the analysis of complex data sets. This is largely due to the development of Markov chain Monte Carlo methods, which expand the scope of application of Bayesian methods considerably. In this paper, we review the Bayesian contributions to inference for point processes. We focus on non-Markovian processes, specifically Poisson and related models, doubly stochastic models, and cluster models. We also discuss Bayesian model selection for these models and give examples in which Bayes factors are applied both directly and indirectly through a reversible jump algorithm.

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Authors and Affiliations

  1. Department of Applied Mathematics, Heidelberg University, Heidelberg, Germany

    Thordis L. Thorarinsdottir

  2. University of Washington, Seattle, WA, USA

    Peter Guttorp

  3. Norwegian Computing Centre, Oslo, Norway

    Peter Guttorp

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  1. Peter Guttorp
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  2. Thordis L. Thorarinsdottir
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Correspondence to Thordis L. Thorarinsdottir .

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Editors and Affiliations

  1. Facultad de Derecho y Ciencias Sociales, Área de Estadística, Universidad de Castilla la Mancha, Avenida Camilo Jose Cela 14, Ciudad Real, 13005, Spain

    Emilio Porcu

  2. , Statistics, Universidad de Castilla la Mancha, Cobertizo San Pedro Martir, Toledo, 45071, Spain

    José–María Montero

  3. , Mathematics Stochastics, Universität Göttingen, Goldschmidtstrasse 7, Göttingen, 37077, Germany

    Martin Schlather

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Guttorp, P., Thorarinsdottir, T.L. (2012). Bayesian Inference for Non-Markovian Point Processes. In: Porcu, E., Montero, J., Schlather, M. (eds) Advances and Challenges in Space-time Modelling of Natural Events. Lecture Notes in Statistics(), vol 207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17086-7_4

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