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Dynamic multiscale spatiotemporal models for Poisson data
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Fonseca, Thaís C. O. and Ferreira, Marco A. R. (2017) Dynamic multiscale spatiotemporal models for Poisson data. Journal of the American Statistical Association, 112 (517). pp. 215-234. doi:10.1080/01621459.2015.1129968 ISSN 0162-1459.
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WRAP-dynamic-multiscale-spatiotemporal-models-Poisson-data-Fonseca-2017.pdf - Accepted Version - Requires a PDF viewer. Download (3850Kb) | Preview |
Official URL: http://dx.doi.org/10.1080/01621459.2015.1129968
Abstract
We propose a new class of dynamic multiscale models for Poisson spatiotemporal processes. Specifically, we use a multiscale spatial Poisson factorization to decompose the Poisson process at each time point into spatiotemporal multiscale coefficients. We then connect these spatiotemporal multiscale coefficients through time with a novel Dirichlet evolution. Further, we propose a simulation-based full Bayesian posterior analysis. In particular, we develop filtering equations for updating of information forward in time and smoothing equations for integration of information backward in time, and use these equations to develop a forward filter backward sampler for the spatiotemporal multiscale coefficients. Because the multiscale coefficients are conditionally independent a posteriori, our full Bayesian posterior analysis is scalable, computationally efficient, and highly parallelizable. Moreover, the Dirichlet evolution of each spatiotemporal multiscale coefficient is parametrized by a discount factor that encodes the relevance of the temporal evolution of the spatiotemporal multiscale coefficient. Therefore, the analysis of discount factors provides a powerful way to identify regions with distinctive spatiotemporal dynamics. Finally, we illustrate the usefulness of our multiscale spatiotemporal Poisson methodology with two applications. The first application examines mortality ratios in the state of Missouri, and the second application considers tornado reports in the American Midwest.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
| Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Big data, Monte Carlo method, Multiscale modeling, Time-series analysis, Poisson processes | |||||||||
| Journal or Publication Title: | Journal of the American Statistical Association | |||||||||
| Publisher: | American Statistical Association | |||||||||
| ISSN: | 0162-1459 | |||||||||
| Official Date: | 2017 | |||||||||
| Dates: |
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| Volume: | 112 | |||||||||
| Number: | 517 | |||||||||
| Page Range: | pp. 215-234 | |||||||||
| DOI: | 10.1080/01621459.2015.1129968 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 03 May 2017, available online: http://www.tandfonline.com/10.1080/01621459.2015.1129968. | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 13 November 2019 | |||||||||
| Date of first compliant Open Access: | 19 November 2019 | |||||||||
| RIOXX Funder/Project Grant: |
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