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H 1 High-dimensional Bayesian geostatistics ​

Auteurs : Banerjee, Sudipto (Auteur de la Conférence)
CIRM (Editeur )

Résumé : With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understand the complex nature of spatial and temporal variability. However, fitting hierarchical spatiotemporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. I will present a focused review of two methods for constructing well-defined highly scalable spatiotemporal stochastic processes. Both these processes can be used as priors" for spatiotemporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparse precision matrices for its finite realizations. Both processes can be exploited as a scalable prior embedded within a rich hierarchical modeling framework to deliver full Bayesian inference. These approaches can be described as model-based solutions for big spatiotemporal datasets. The models ensure that the algorithmic complexity has n floating point operations (flops), where n is the number of spatial locations (per iteration). We compare these methods and provide some insight into their methodological underpinnings.

Keywords : Bayesian modeling; directed acyclic graphs; Gaussian processes; low-rank models; scalable models; spatial stochastic processes

Codes MSC :
62F15 - Bayesian inference
62M30 - Statistics of spatial processes
62P12 - Applications of statistics to environnemental and related topics

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 06/12/2018 Date de captation : 29/11/2018 Collection : Research talks Format : MP4 Durée : 01:00:45 Domaine : Probability & Statistics Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2018-11-29_Banerjee.mp4 Informations sur la rencontre Nom de la rencontre : Jean-Morlet chair: Bayesian statistics in the big data era / Chaire Jean-Morlet : Statistiques bayésiennes à l'ère du big data Organisateurs de la rencontre : Freyemurth, Jean-Marc ; Marin, Jean-Michel ; Mengersen, Kerrie ; Pommeret, Denys ; Pudlo, PierreDates : 26/11/2018 - 30/11/2018 Année de la rencontre : 2018 URL Congrès : https://www.chairejeanmorlet.com/2018-2-...Citation Data DOI : 10.24350/CIRM.V.19478503 Cite this video as: Banerjee, Sudipto (2018). High-dimensional Bayesian geostatistics ​. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19478503 URI : http://dx.doi.org/10.24350/CIRM.V.19478503

### Voir aussi

Bibliographie

1. Banerjee, S. (2017). High-dimensional Bayesian geostatistics. Bayesian Analysis, 12(2), 583-614 - https://doi.org/10.1214/17-BA1056R

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