Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the nonsparse nature of the covariance matrix. We derive a fast approximation of the likelihood for such models.We propose to sample from the approximate posterior (i.e., the prior times the approximate likelihood), and then to recover the exact posterior through importance sampling.We show that the variance of the importance sampling weights vanishes as the sample size goes to infinity. We explain why the approximate posterior may typically be multimodal, and we derive a Sequential Monte Carlo sampler based on an annealing sequence to sample from that target distribution. Performance of the overall approach is evaluated on simulated and real datasets. In addition, for one real-world dataset, we provide some numerical evidence that a Bayesian approach to semiparametric estimation of spectral density may provide more reasonable results than its frequentist counterparts. The article comes with supplementary materials, available online, that contain an Appendix with a proof of our main Theorem, a Python package that implements the proposed procedure, and the Ethernet dataset. © 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Computational Aspects of Bayesian Spectral Density Estimation / N., Chopin; J., Rousseau; Liseo, Brunero. - In: JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS. - ISSN 1061-8600. - STAMPA. - 22:3(2013), pp. 533-557. [10.1080/10618600.2013.785293]

Computational Aspects of Bayesian Spectral Density Estimation

LISEO, Brunero
2013

Abstract

Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the nonsparse nature of the covariance matrix. We derive a fast approximation of the likelihood for such models.We propose to sample from the approximate posterior (i.e., the prior times the approximate likelihood), and then to recover the exact posterior through importance sampling.We show that the variance of the importance sampling weights vanishes as the sample size goes to infinity. We explain why the approximate posterior may typically be multimodal, and we derive a Sequential Monte Carlo sampler based on an annealing sequence to sample from that target distribution. Performance of the overall approach is evaluated on simulated and real datasets. In addition, for one real-world dataset, we provide some numerical evidence that a Bayesian approach to semiparametric estimation of spectral density may provide more reasonable results than its frequentist counterparts. The article comes with supplementary materials, available online, that contain an Appendix with a proof of our main Theorem, a Python package that implements the proposed procedure, and the Ethernet dataset. © 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
2013
sequential monte carlo; fexp; long-memory processes
01 Pubblicazione su rivista::01a Articolo in rivista
Computational Aspects of Bayesian Spectral Density Estimation / N., Chopin; J., Rousseau; Liseo, Brunero. - In: JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS. - ISSN 1061-8600. - STAMPA. - 22:3(2013), pp. 533-557. [10.1080/10618600.2013.785293]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/531128
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