Statistical Modelling 9 (2009), 325
Modelling zero-inflated spatio-temporal processes
Marcus VM Fernandes
IBGE
Brazil
Alexandra M Schmidt
Departamento de Métodos Estatísticos,
Universidade Federal do Rio de Janeiro,
Caixa Postal 68530, CEP 21945-970,
Rio de Janeiro, RJ
Brazil
eMail:
alex@im.ufrj.br
Helio S Migon
COPPEUFRJ
Brazil
Abstract:
We consider models for spatio-temporal processes which
assume either non-negative values, and often are observed as zero,
or discrete values and are also inflated by zeros. Typically, in the
first case, the spatial observations are obtained at fixed locations
(point-referenced data) over a region D; whereas in the second,
the region D is divided into a finite number of regular or
irregular subregions (areal level), resulting in observations for each
subregion. Our main idea is based on those of zeroinflated models, by
assuming that the value observed at location s and time
t, Yt (s), is a realization of a mixture
between a Bernoulli distribution with a probability of success
θt (s) and a probability density function or
probability function p(yt (s) | .)
For both cases, we include spatio-temporal latent processes in the model
to account for the possible extra variation present in the mean structure
of θt (s)
and/or p(yt(s) | .).
In the context of point-referenced data, we model the amount of rainfall
over the city of Rio de Janeiro during 75 weeks; whereas in the areal data
level case, we consider weekly cases of dengue fever in the city of Rio de
Janeiro during the years of 2001–02.
Keywords:
Bayesian paradigm; conditional autoregressive processes;
gaussian processes; mixture models; model comparison
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