2,865 research outputs found
A dynamic nonstationary spatio-temporal model for short term prediction of precipitation
Precipitation is a complex physical process that varies in space and time.
Predictions and interpolations at unobserved times and/or locations help to
solve important problems in many areas. In this paper, we present a
hierarchical Bayesian model for spatio-temporal data and apply it to obtain
short term predictions of rainfall. The model incorporates physical knowledge
about the underlying processes that determine rainfall, such as advection,
diffusion and convection. It is based on a temporal autoregressive convolution
with spatially colored and temporally white innovations. By linking the
advection parameter of the convolution kernel to an external wind vector, the
model is temporally nonstationary. Further, it allows for nonseparable and
anisotropic covariance structures. With the help of the Voronoi tessellation,
we construct a natural parametrization, that is, space as well as time
resolution consistent, for data lying on irregular grid points. In the
application, the statistical model combines forecasts of three other
meteorological variables obtained from a numerical weather prediction model
with past precipitation observations. The model is then used to predict
three-hourly precipitation over 24 hours. It performs better than a separable,
stationary and isotropic version, and it performs comparably to a deterministic
numerical weather prediction model for precipitation and has the advantage that
it quantifies prediction uncertainty.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS564 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bayesian Semiparametric Hierarchical Empirical Likelihood Spatial Models
We introduce a general hierarchical Bayesian framework that incorporates a
flexible nonparametric data model specification through the use of empirical
likelihood methodology, which we term semiparametric hierarchical empirical
likelihood (SHEL) models. Although general dependence structures can be readily
accommodated, we focus on spatial modeling, a relatively underdeveloped area in
the empirical likelihood literature. Importantly, the models we develop
naturally accommodate spatial association on irregular lattices and irregularly
spaced point-referenced data. We illustrate our proposed framework by means of
a simulation study and through three real data examples. First, we develop a
spatial Fay-Herriot model in the SHEL framework and apply it to the problem of
small area estimation in the American Community Survey. Next, we illustrate the
SHEL model in the context of areal data (on an irregular lattice) through the
North Carolina sudden infant death syndrome (SIDS) dataset. Finally, we analyze
a point-referenced dataset from the North American Breeding Bird survey that
considers dove counts for the state of Missouri. In all cases, we demonstrate
superior performance of our model, in terms of mean squared prediction error,
over standard parametric analyses.Comment: 29 pages, 3 figue
Statistical Modeling of Spatial Extremes
The areal modeling of the extremes of a natural process such as rainfall or
temperature is important in environmental statistics; for example,
understanding extreme areal rainfall is crucial in flood protection. This
article reviews recent progress in the statistical modeling of spatial
extremes, starting with sketches of the necessary elements of extreme value
statistics and geostatistics. The main types of statistical models thus far
proposed, based on latent variables, on copulas and on spatial max-stable
processes, are described and then are compared by application to a data set on
rainfall in Switzerland. Whereas latent variable modeling allows a better fit
to marginal distributions, it fits the joint distributions of extremes poorly,
so appropriately-chosen copula or max-stable models seem essential for
successful spatial modeling of extremes.Comment: Published in at http://dx.doi.org/10.1214/11-STS376 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A Bayesian space-time model for discrete spread processes on a lattice
Funding for this work was provided by GEOIDE through the Government of Canada’s Networks for Centres of Excellence program.In this article we present a Bayesian Markov model for investigating environmental spread processes. We formulate a model where the spread of a disease over a heterogeneous landscape through time is represented as a probabilistic function of two processes: local diffusion and random-jump dispersal. This formulation represents two mechanisms of spread which result in highly peaked and long-tailed distributions of dispersal distances (i.e., local and long-distance spread), commonly observed in the spread of infectious diseases and biological invasions. We demonstrate the properties of this model using a simulation experiment and an empirical case study - the spread of mountain pine beetle in western Canada. Posterior predictive checking was used to validate the number of newly inhabited regions in each time period. The model performed well in the simulation study in which a goodness-of-fit statistic measuring the number of newly inhabited regions in each time interval fell within the 95% posterior predictive credible interval in over 97% of simulations. The case study of a mountain pine beetle infestation in western Canada (1999-2009) extended the base model in two ways. First, spatial covariates thought to impact the local diffusion parameters, elevation and forest cover, were included in the model. Second, a refined definition for translocation or jump-dispersal based on mountain pine beetle ecology was incorporated improving the fit of the model. Posterior predictive checks on the mountain pine beetle model found that the observed goodness-of-fit test statistic fell within the 95% posterior predictive credible interval for 8 out of 10. years. The simulation study and case study provide evidence that the model presented here is both robust and flexible; and is therefore appropriate for a wide range of spread processes in epidemiology and ecology.PostprintPeer reviewe
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