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Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal

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  • Kostas Triantafyllopoulos

Abstract

The purpose of this paper is to provide a critical discussion on real‐time estimation of dynamic generalized linear models. We describe and contrast three estimation schemes, the first of which is based on conjugate analysis and linear Bayes methods, the second based on posterior mode estimation, and the third based on sequential Monte Carlo sampling methods, also known as particle filters. For the first scheme, we give a summary of inference components, such as prior/posterior and forecast densities, for the most common response distributions. Considering data of arrivals of tourists in Cyprus, we illustrate the Poisson model, providing a comparative analysis of the above three schemes. L'objectif de cet article est de fournir une discussion critique sur l'estimation en temps réel de modèles dynamiques linéaires généralisés. Trois approches pour faire l'estimation sont décrites et comparées, la première étant basée sur l'analyse conjuguée et les méthodes de Bayes linéaires, la deuxième sur l'estimation postérieure de modes, et la troisième sur des méthodes Monte‐Carlo d'échantillonnage séquentiel, aussi connues comme filtres particulaires. Pour la première approche, on donne un résumé des composants d'inférence, telles que les densités antérieures/postérieures et prévisionnelles, pour les distributions de réponse les plus communes. À partir de données sur l'arrivée de touristes à Chypre, on illustre le modèle de Poisson, tout en fournissant une analyse qui compare les trois approches.

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  • Kostas Triantafyllopoulos, 2009. "Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal," International Statistical Review, International Statistical Institute, vol. 77(3), pages 430-450, December.
    • Handle: RePEc:bla:istatr:v:77:y:2009:i:3:p:430-450
    DOI: 10.1111/j.1751-5823.2009.00087.x
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    1. Benjamin Kearns & Matt D. Stevenson & Kostas Triantafyllopoulos & Andrea Manca, 2019. "Generalized Linear Models for Flexible Parametric Modeling of the Hazard Function," Medical Decision Making, , vol. 39(7), pages 867-878, October.
    2. James D. Santos & José M. J. Costa, 2019. "An Algorithm for Prior Elicitation in Dynamic Bayesian Models for Proportions with the Logit Link Function," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 169-183, March.
    3. Andrés R. Masegosa & Darío Ramos-López & Antonio Salmerón & Helge Langseth & Thomas D. Nielsen, 2020. "Variational Inference over Nonstationary Data Streams for Exponential Family Models," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
    4. Mike West, 2020. "Bayesian forecasting of multivariate time series: scalability, structure uncertainty and decisions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 1-31, February.

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