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Open AccessArticle

Prior Sensitivity Analysis in a Semi-Parametric Integer-Valued Time Series Model

1
Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo 05508-090, Brazil
2
Department of Decision Sciences and BIDSA, Bocconi University, via Röntgen 1, 20136 Milano, Italy
3
Insper Institute of Education and Research, Rua Quatá 300, São Paulo 04546-042, Brazil
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(1), 69; https://doi.org/10.3390/e22010069
Received: 26 November 2019 / Revised: 23 December 2019 / Accepted: 3 January 2020 / Published: 6 January 2020
(This article belongs to the Special Issue Data Science: Measuring Uncertainties)
We examine issues of prior sensitivity in a semi-parametric hierarchical extension of the INAR(p) model with innovation rates clustered according to a Pitman–Yor process placed at the top of the model hierarchy. Our main finding is a graphical criterion that guides the specification of the hyperparameters of the Pitman–Yor process base measure. We show how the discount and concentration parameters interact with the chosen base measure to yield a gain in terms of the robustness of the inferential results. The forecasting performance of the model is exemplified in the analysis of a time series of worldwide earthquake events, for which the new model outperforms the original INAR(p) model. View Full-Text
Keywords: time series of counts; Bayesian hierarchical modeling; Bayesian nonparametrics; Pitman–Yor process; prior sensitivity; clustering; Bayesian forecasting time series of counts; Bayesian hierarchical modeling; Bayesian nonparametrics; Pitman–Yor process; prior sensitivity; clustering; Bayesian forecasting
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Graziadei, H.; Lijoi, A.; Lopes, H.F.; Marques F., P.C.; Prünster, I. Prior Sensitivity Analysis in a Semi-Parametric Integer-Valued Time Series Model. Entropy 2020, 22, 69.

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