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CATEGORIES:Statistics
SUMMARY:High-Dimensional Bayesian Geostatistics - Sudipto
Banerjee (UCLA)
DTSTART;TZID=Europe/London:20170123T160000
DTEND;TZID=Europe/London:20170123T170000
UID:TALK70609AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/70609
DESCRIPTION:With the growing capabilities of Geographic Inform
ation Systems (GIS) and user-friendly software\, s
tatisticians today routinely encounter geographica
lly referenced data containing observations from a
large number of spatial locations and time points
. Over the last decade\, hierarchical spatial-temp
oral process models have become widely deployed st
atistical tools for researchers to better understa
nding the complex nature of spatial and temporal v
ariability. However\, fitting hierarchical spatial
-temporal models often involves expensive matrix c
omputations with complexity increasing in cubic or
der for the number of spatial locations and tempor
al points. This renders such models unfeasible for
large data sets. In this talk\, I will present so
me approaches for constructing well-defined spatia
l-temporal stochastic processes that accrue substa
ntial computational savings. These processes can b
e used as "priors" for spatial-temporal random fie
lds. Specifically\, we will discuss and distinguis
h between two paradigms: low-rank and sparsity and
argue in favor of the latter for achieving massiv
ely scalable inference. We construct a well-define
d Nearest-Neighbor Gaussian Process (NNGP) that ca
n be exploited as a dimension-reducing prior embed
ded within a rich and flexible hierarchical modeli
ng framework to deliver exact Bayesian inference.
Both these approaches lead to algorithms with floa
ting point operations (flops) that are linear in t
he number of spatial locations (per iteration). We
compare these methods and demonstrate their use i
n a number of applications and\, in particular\, i
n inferring on the spatial-temporal distribution o
f air pollution in continental Europe using spatia
l-temporal regression models in conjunction with c
hemistry transport models.\n\nThis is based upon j
oint work with Abhirup Datta (Johns Hopkins Univer
sity) and Andrew O. Finley (Michigan State Univers
ity)
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge.
CONTACT:Quentin Berthet
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